Purchasing speed by buying a bike

Yes......the difference would be seen mostly in aerodynamics and weight.....as well as rolling resistance.  So there are significant gains to be made by upgrading to even the most entry level of road bikes (Trek 1.2, 2.1, etc.)

If you put Lance Armstrong on a hybrid he could not win the TdF.......if you put him on a Trek 2.1 he'd have a much better shot.

I would say in general, yes.  I just did the same thing...went from a Gary Fisher hybrid to a Fuji road bike.  I would say I'm 1-2 mph faster right now, but I'm still learning to ride in the much more aggressive position that a road bike has (and this road bike in particular has pretty aggressive geometry).  I had also made the hybrid as fast as possible, with road tires and clip-on aerobars.

I upgraded from a hybrid to a 5 year old used Bianchi road bike (aluminum frame).  Paid around $200 for it off of craigslist.  I'd estimate approximately 2-3 mph avg improvement immediately.

It was worth it.

That's it exactly - I go 12-15 with an average closer to 12.  It's hard work and tough to believe it's only my fitness getting in the way (not that I don't need to build - a lot).  For training maybe it doesn't matter - whether you go 10 miles or 15, the same amount of effort will net you the same benefit. But obviously for a race it matters.

I can hear my checking account weeping in the distance...

Here's a counterpoint to all the "a road bike is the only way to go" input.

When I was bike racing, we rode year-round. I had an old mountain bike that I turned into what I called an "urban assault bike". I put drop bars on it, with standard road brake levers and bar end shifters, 1.5" slick tires at 70 psi, and full fenders (and I do mean FULL fenders), all parts I had laying around from other bike projects. And I had no problems keeping up on those wet winter rides with my team mates.

I guess what I'm saying is that there are ways you can modify the bike you have inexpensively and most likely gain 90% of what you'd get with a road bike. It'll still be a bit heavier, but we've gone over the "weight issue in triathlon" many times -- it's not that big of a deal.

In racing sports- every racing sport- the famous Carroll Shelby quote applies:

"Speed costs money. How fast do you want to go?"

That said, racing cars (Carroll Shelby is a race car designer) is much more equipment dependent than triathlons.

Or is it...

If you look at the multi-hundred million dollar budget of a Formula 1 team and consider the team will spend literally millions to gain a tenth of a second per lap then it become analogous to our sport.

A good basic bike with a proper fit gets you most of the way the there. Of course, the majority of speed eminates from the riders' fitness. The biggest gains are almost always fitness gains. But fitness has an attendent cost too: Time, power meters, coaches, training camps, nutritional products, massages, etc. If you devoted $10,000 to those resources there would likely be a measureable improvement in your performance if you're adequately motivated.

How much difference can a bike make? Tough to say. Depends on what you're coming off of and going on to. I'll always quote the party line that the single largest improvement opportunity is through good bike fit (after fitness, of course). So that is where I would start- with a good fit and position. From there, look firstly at what you're wearing: Is your on-bike race uniform aerodynamic? That's key- and less expensive than a new bike and aerodynamic wheels.

It's possible to write volumes on this topic and the subject is a moving target as our ability to understand what makes an athlete fast on a bike improves. I will suggest there is general consensus on fit and position being at least significant, if not critical.

After my first race, when I was on everyone elses right, I got a new bike that same day.  I can't say how much faster I am going, I'll just say there is actually wind in my hair when I ride, even when it isn't there when I stop.

Looking forward to my second race.... maybe I won't be dead last in my AG.

Tom, it was partly your excellent thread on "our biggest delimiter" that made me question whether a new bike would make that much difference - that and many other people's observation that it is the engine that counts.  FWIW, I'm currently on a Trek 7100 that I love for its comfort and ride.  The LBS made a few adjustments but I've never been fitted.  I'd be going to whatever looked good on craigslist.  The plan would be to go to the LBS, get recommendations on size, and then watch craigslist to see what pops up.  Then pay for a tune-up, and yes, a fitting.  Jeez this is adding up.

Clothes are aerodynamic except possibly the windbreaker.  Won't be an issue as the weather warms up.

If you buy a new bike, do they fit it to you as part of the price? 

The party line is often propaganda.

Beside any improvement in speed or any other technical advantage that you may get with a new bike, the biggest benefit will be that if you are happy with it and you like it you will ride more and harder.  And that will make you faster.....

Yes of course, there are a lot of people around here that will tell you its all about the motor and not the bike.  But if you take a 300hp motor and put it in a 10000lb delivery truck its not going to go fast or handle well. Take the same 300hp motor and put it in a 3000lb sports car and you are going much faster. Its just a fact of physics.

That doesnt mean that you can get away with not training. You still need to work hard to develop the 300hp.

x2...I topped out on my hybrid on downhills all the time.  Not so much with the 50/11 gear ratio on the roadie.

Your gear won't suddenly turn you into Macca or Kemper, but better gear will raise the ceiling of what is possible for you to do.  You just have to be willing to push yourself to achieve those higher possibilities.

Bad Gear + Hard Work = Good

Good Gear + No Work = Waste of Money

Good Gear + Hard Work = SUCCESS

Not that big a deal. Maybe if you're starting from a sedentary couch potato, but otherwise if you've been training semi-seriously for a couple of seasons most folks have already reaped a large hunk of all the fitness gains they're ever going to see. If you fall into that group the gains you see (in cycling) from reducing drag of various sources is going to be larger than what you're going to get from fitness gains. That's especially true if (like the OP) your starting point is a hybrid bike. It's not unusual to see a (normal-sized) guy on a hybrid bike with a CdA of .35+ (and Crr > .006 to boot). Put him in a good position on a top TT bike with good tires/tubes and you're looking at a CdA < .25; top guys way less. You'd have to be hoping to reap a pretty big gain in fitness to top that. 

Right, but another way to think of it is to standardize for distance by looking at savings per km. For most courses, whether long course or short, the bike leg is 4x longer than the run. So, if you save 1 sec/km on the bike, that's equivalent to running 4 sec/km faster. The difference between a typical hybrid bike position and a good TT bike position can be more than 10 sec/km at the same power. Your run pace would have to improve by 40 sec/km (= 1 min/mile) just to match that.