Getting faster on the bike

THird everything that Rick said.  One long ride, one interval ride where you are working at a higher intensity ( near your LT) beginning with 8 or 10 min intervals and increasing the work interval as able with a few minutes recovery between intervals are great for increasing speed.  Hills at a lower cadence build strength,  "spinning" up hills at a higher cadence is good race strategy practice.  Recovery ride if you can fit one in and still get your run and swim training.

Do spin in the winter when you can't ride. 

Start working on ILT to help smooth you stroke.  Start doing reps, intervals, hills, ride more.

Something else to think about, is you don't know who all was at that race.  So 17-19 MPH could be fantastic.  But if you really want to get faster, it is likely going to take more miles.

Spin classes are great for areobic workouts, but not great for building speed.

How is your bike set up?  Do you have aero bars?  If not get some, that alone should cut some time off your ride (some posters say it is worth 2 MPH.)

A typical spin class has a lot of anaerobic intervals...short, hard bursts.  Those have thier place, don't get me wrong, but how often are you anaerobic during an Olympic distance race on the bike?  Hopefully not often, because if you do it too much you will blow up and run poorly.  Biking in a tri is more about being able to maintain a consistent (hopefully fast ) speed at a low intensity. 

I teach spin in the winter and it's a good calorie burner, breaks things up and makes my workouts less boring. It's also useful for strength workouts....low cadence high resistance "climbs".  LTs can be done on a spin bike as well, but aren't part of most spin instructor's plans because they're boring and they hurt...good way to lose customers   So I don't mess around with spinning in the summer when I can be out on my bike, other than subbing once in awhile to help out.  

For the OP, if you want to ride fast spend more time riding, ride long ride short, ride easy and very few days ride hard. First be sure you can ride your goal distance and longer with ease. Make sure you ride it at a steady pace and the next day you feel you can do it again. As Mike R says all the time: “Be consistent and work on the base” Once you accomplish that then you can start adding more variety/intensity to your training which will enhance it not limit it…

Rick and Jorge said it best.  Just also remember that "fast" is a relative term in cycling.  YOu can be fast over a 40k TT.  You can be fast up hill climbs.  You can be fast on breakaway sprints.  You can be fast over an entire race.  You can be a fast decender.  The list goes on.  Each form of fast requires different types of training.

Original Poster

In addition to "ride lots" (credit Bear) I would suggest having your bike fit analyzed at your local bike shop.  I recently had my bike fit at a shop that specializes in tri bikes and it has made a huge difference for me in terms of overall comfort on the bike and my average speed.  My old setup was using my hamstrings too much whereas now my bike power is coming from my quads, as it should have been all along.  I also have a Trek 1500.  Hope this helps.