No way in hell I'd kill myself after a zombie bite.
First of all, those last few minutes would be precious to me because, well, they'd be my last few minutes.
Plus, suicide is wrong.
And finally, I'm not taking the chance that I'm delusional and that there is really no such thing as zombies. If I'm wrong, after I'm dead and zombified, my shambling corpse will be someone else's problem.