How do I improve my bike?

Congrats.  Long Beach was one of my first ones as well

While you're waiting to trade up to new gear, there's what the rest of us had to do....

ride lots.  Then ride some more.  There's no other way to get faster, especially starting out.

OP says she has road tires already.

X2 what Chris said - ride, ride, ride

How often are you riding now, and what distances?

I'm convinced that some people are born with flat-land speed, and others aren't.  Although riding more will help for sure, there are just some people that haul on the relatively flat and downhill stuff.  Check out some group rides, too.  Riding with faster people will make you faster.

I wish I could find a triathlon that had an entirely uphill bike.

Almost

http://www.alpetriathlon.com/spip/?lang=en

Man, that's great.  I may have to get my passport renewed afterall.

jeebus Chris, and I thought I had hills... 

unfortunately it has french commentory but on this page you'll find  video  coverage of this years Alpe d'Huez 

http://www.triclair.com/videos/telechargement-videos-triathlon.php

Sometimes it takes a few goes to get the file to download but it does in the end. 

As has been said before:

Ride, Ride, Ride.

I would also highly recommend either pedals and shoes or at least cages on your current pedals.

Michael

I'm still new to triathlons, but I do have experience with mtn bike versus used Cervelo (me on the mtn bike, my friend who's a busy surgical resident on the Cervelo.)

Me: I run an 18:30 5k

 Friend: He runs a 23:00 5k

 Both of us have similar bike background, which is little. Me on a mtn bike, him on a road bike, but I probably have rode a lot more than him this year due to his crazy busy schedule.

On a 40 minute road ride, I couldn't stay with him even at ALL-OUT effort on my mtn bike. He cruised without even trying to drop me, and waited for me a lot, but his aerobike was literally so much faster that even with my superior VO2/endurance, I had absolutely no chance on the bike. Humbled me big time - I'd assumed that my mtn bike "handicap" would equalize our physical differences. (I was running 70 miles per week as well at the time and was in shape to run a 3:10 marathon, or 7:15/mile x 26 miles.) 

Point of story as someone (many people) pointed out to me: don't bring a knife to a gun fight, or a mtn bike to a road bike race. It'll get you through to the finish, but you won't be able to compete at the level you deserve once you're training.

Get one of these like I just did and you'll be ready for some instant mega-payback to all those folks who passed you at Long beach.

As a newbie to the aero position as well, I'll also mention to you that if you're going to invest some serious time on the bike in training, you should seriously consider an aerobike if you're only going to do triathlons. The positioning is very aggressive and for anything longer than a sprint, you really have to train in that position to take advantage of it. I'm a fairly solid mtn biker and even occasional road biker, but the aero position is so new to me that even with the pro-fitted bike above, I suspect that I'm currently slower on the aerobike than a pure road bike, since I still feel unstable and somewhat uncomfortable in the aero position. (Ask me how I feel after training on it for the next months though!) 

As everyone already said, new bike road/tri will help you out.  Until then.. make sure you have an interval day in your weekly routine. You won't race faster if you don't train faster...

On the flats, do you know what your cadence was? Most people recommend spinning 85-95 rpms...

When you say spinning at 85-95 rpms, does that mean 8.5 - 9.5?  My cadence thing relays cadence to me like this...  8.9   .9.1   never 90 or  95 

 is it the same thing?

They forgot to tell you the real secret to improving your bike, paint it red. Every cyclist knows that red bikes are faster! Just kidding, but a good road or tri bike will make a huge difference and clipless pedals are a given. Besides the basic investment, ride lots, work your way into riding with groups-you'll catch on to the cadence by cycling. I don't have to look at my cadence, with time you know it. You learn it by doing what the good riders do. When you ride in groups you catch onto the cadence that the more experienced good riders do at a given speed and gear accordingly.

Step 1. Get a good bike

Step 2. ride lots

Step 3. Ride very hard sometimes (varied paces)

PS Don't throw down big bucks on your first road/tri bike.  A $1000 road bike will go nearly as fast as a $4000 road bike for 90% of the riders (certainly within 1mph) - it is the engine that gives the best return on investment.

And log your workouts so we can be more helpful as you progress