Great advice from Boydie as always. I thought I'd chip in and say that my singing is SO much better without headphones, that I intend on refusing ever recording with them again. In fact, it goes for any overdubbing/ recording. I use speakers for everything except acoustic guitar now, because hearing the song naturally allows more space for a good performance, not to mention time keeping. I don't know what it is about phones, but they suck the life out of me...
So yep, forget about bleed - any live recording has it in spades anyway, and learning to deal with it, or even take advantage of it will only make you a better producer in the long run.