So Really...How much Does the Bike Matter

it's a cliche, but it's true-- "It's all about the engine". There are absolutely gains to be made with a tri bike due to the better positioning, but for someone new the low-hanging fruit is working on the engine. I think it's solid advice to not pour a bunch of money into the sport until you're sure that you're into it for years to come.

My bigger concern is you comment about not being comfortable, even after a fitting. You mentioned that you bought online. Did the fitter say anything about the bike not being an ideal fit that he had to just work with? What kind of discomfort? Some discomfort will go away with conditioning, but if it's serious mention it to the fitter.

With regards to triathlon, the bike frame itself is a very small factor.  It's more about the position the bike can put you in, as you the rider, make up for around 90% of the overall aerodynamic drag that you will experience while on the bike.

If buying a more expensive bike puts you in a better position, you should be faster...maybe significantly faster.  But if buying a new bike does not change your position, you're probably splitting hairs, and any speed increase you might see, may not even be noticeable.  

More expensive bikes generally come stock with nice rolling tires...so that can play a pretty big role in how fast the bike actually rides, but it's not to say that the bike frame is actually that much faster.  More expensive bikes also come with better componentry, which will make the shifting a lot smoother, but in general won't give you very much, if any speed increases assuming you take care of your drive train.

Most of the best fitters available...don't even sell bikes.  They sell their service of fitting, and let you decide what bike you want to buy after that with no strings attached.

Granted, these types of fitters are not widely available in all areas.  You may very well need to use a fitter that does work for a bike shop, but again, that doesn't mean you need to buy a bike from them.  If they charge you for a fitting, that's all you should get.  Some bike shops do offset some or all of the fitting cost if you do end up buying a bike from them.  Main thing is to talk out your situation ahead of time so expectations are set.

Honestly, if you went from your bike now to a top-end, perfectly fitted $15k ubertribike with aero everything, you'd maybe go from 56th/100 in the bike to MAYBE 40-45th/100. More realistically, like 45/50th. 

The gains from a faster bike are real, but they're still small, like 1-2 minutes per hour of racing, which in a typical Oly-distance race means saving 60-90 seconds on the bike split. If you're coming from a really suboptimal bike fit, you'll get more than that, but highly unlikely to get 4+ minutes/hr of racing unless you're coming from a mtn bike to tribike.

^^That

More gains than that are not impossible, but do know that the money for performance goes up fast with bikes. A lot of the major bikes have frames a step or two off their flagship that can really keep a LOT of their performance (and some further down the line too). Think more "reasonably well" in performance as many bikes can within the last few years can do that quite well. Then the more important part would be how well it fits. You should get some more power out of it right away, and also since it should fit more comfortably you'll likely be able to push yourself both harder and more often, leading to more gains through better training sessions.

What Jason said on the fitting. The more advanced fitting sessions available now aren't so much putting you so directly on a bike, but finding the position. What they use isn't really a bike, but a set of rails to put on pedals, a saddle and some handle bars. They should be able to give you a set of spacial coordinates that relates your various contact points. Meaning the saddle to the bottom bracket & pedals, and also to the elbow pads & bars. These are all your contact points with the bike. They find your position and from there can help with what bikes should fit well without having to go all wonky with stems and other parts. The various bike manufactures will have the dimensions of their frames & bikes and the fitter should have this information and know how to make it work with the various parts you can swap in. A shop that sells bikes will show how theirs fit. Not necessarily a bad things, just is. They should still be able to give you the coordinates. 

This year I've been in the top 3 for bike splits on a straight-up roadie. Did use race wheels, but no clip-ons. Kept the torso fairly low and the rest is in a good position to produce lots of power. Frame is terribly un-aero too as the down tube nearly hides a standard water bottle.

Depending on the course and the race he usually averages 25-26.5 on his road bike over sprint distance.  He went from a 58 bike, that only margionally fit him, to a 61 in the Madone that fits him much better and probably gained about .5 - 1 mph (about a $3000 upgrade)....but it's a MUCH better fit.(still tweaking it)  In keeping with the discussion, he can do a sprint distance time trial on his 2010 P2 in 27-28.5, again, depending on course, wind, etc. (mph is not the greatest metric) His fit on that bike is REALLY good.

Here's the elephant in the room.......

GETTING FASTER ON A BIKE IS REALLY HARD WORK! 

You can buy all the speed you think you can afford, but if you don't spend at least some part of every ride on the bike feeling like you are ready to puke, you have left some gains on the table.  It's a bike.....you are not pounding your body.....ride it like you stole it!

As much as I despise the stupid triathlon sayings, it really is all about the engine.  (and your fit on the bike)

There are not many that do it, but the fitters who can generate enough business are using something like this.  The fitter still needs to be qualified in how to use it, but assuming they do, it makes their job and the experience with the customer much better during the fit session.  No need to swap parts, loosen bolts, and tighten them again.  There are just a bunch of knobs to turn that can instantly adjust the fit coordinates and spit back out a measurement down to the millimeter.  These tools also generally have a built in power meter of some sort so the fitter and customer can see how their power output changes given various positions.  These changes can often be made on the fly, while the customer is still pedaling.

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Your math is correct only if you assume a 1.5 mph gain.  Possible if the OP's position now is pretty bad, and then going to an ideal position, but still an assumption that I don't think yazmaster was making.  So you can't really fault math.  

It's extraordinarily unlike you will gain 5 minutes off a Oly time with aero gear alone. 5 minutes on a 1hr-1:15hr race is almost a whole different category of bike ability. 

The figure of 1-2 minutes gained is already fairly optimistic for most real world conditions. The fast guys are not going fast just because they have the best stuff  they'll be killing the field even on a 1970s round tube bike even with suboptimal fit.