While you could technically use your road bike for triathlon (and definitely should for your first few races), why not use your new hobby as an excuse to head to your local bike shop and pick up the newest tech on the market? Triathlon bikes are created to slice through the wind as aerodynamically and efficiently as possible. But really, those deep rims and sweeping carbon frames just look badass.
Cycling gear aside, it's not much of an investment to get up to speed for the swim and the run. All you really need is a pair of goggles, a tri suit and pair of running shoes. Of course, a wetsuit, nice running socks, a running hat, sunglasses and a race number belt will make the experience more comfortable, but it's not necessary when first starting out