FYI--good times at the Olympic distance (1.5k/40k/10k) for PROFESSIONAL MEN are in the neighborhood of 18:00/58:00/31:00.
The bad news is that you have some work to do on the bike to get to this point. The good news is that you have the two hard sports down. With the aerobic engine you have, you can easily be up to speed (literally) on the bike in a season or two, given the right equipment.
With proper guidance, you could absolutely become an elite level junior or U23 athlete if you wanted to. Keep up the hard work and get yourself a bike!
(To answer your initial question, yes you should get a better bike. Look for at least a road bike with skinny tires and drop handlebars. Try to find some "clip-on aerobars" to make you even more aerodynamic while riding.)