That's what I did! I came out of a horrible relationship, and yelled out loud in my friend's car that I was never dating anyone again. Months later I met my husband now. He had a job, a car, a reasonable house and showed such an initiative to better himself and earn a living. And he was cute too.
My point being, you really never know what's around the corner. As for being bi and looking for one or the other, hm.. I always say that the person who I married could have been either a guy or girl.. it just happened that I clicked with my now-husband and he happened to be a guy. I never looked around for one or the other, per se.
Just immerse yourself in life.. enjoy those pets (it is not a crime for your life to revolve around them, and anyone that you get together with should respect that!) I guess that you just know when that person clicks with you, and if you click with them too.. that's where that's at. If it never happens, that's where life's at, too.