Ditto to the other responders. I, too, was predominantly a runner-only. I then took up swimming and last summer did my first 2 sprint Tri's. The first one I used my trusty old hybrid. I was planning to get a road bike anyway, so I had a road bike for the second Tri. However, until/unless you get hooked on Tri's, I would counsel against buying a road bike or Tri bike lest you be out substantial money for what might be a passing fad.
Incidentally, for what it is worth I believe I am hooked on Tri's and plan to do several this year. If my experience is typical, you may indeed find yourself similarly hooked.