Wasn't going to comment on this thread, but it seems things are skewing one particular way, so I thought I'd share my experience/thoughts. (I'm sure someone else will be looking on here for perspective, even though the OP sounds like she probably would prefer to be without a roommate.)
I think it is VERY MUCH dependent on your personality. If, as you alluded, you are better off having your privacy (and are perhaps more introverted), then not having a roommate is a good idea.
As others have pointed out, if you DO have a roommate, I think it's a good idea that they be a fellow vet student (not necessarily a classmate) or at the very least a grad student in a rigorous program. Even if you spend the majority of your time studying at school/in the lab, you eventually get sick of it and want to study at home at least one or two days before going back to that routine. Living with folks who won't respect or understand your studying is a recipe for disaster.
For myself--and I realize I'm probably the exception--I LOVE my roommate. I was very nervous about finding one, and know that I completely lucked out (trust me, I've had some pretty bad roomie experiences in the past!!). However, for me, living alone wasn't really an option. I tend to be an incredibly gregarious extrovert who gets energized by having other folks around. Because my roommate is also one of my classmates, it's really nice to be able to study together (in silence and then to bounce questions/ideas off of each other), we both know that the apartment gets messy prior to an exam and we don't care, and it's really nice to have someone to whom you can vent about your day/certain professors/etc. I know that if I were living on my own, it'd be easier to procrastinate on the studying and I'd probably take lots of naps! 🙂 That's just me being an extrovert--when I'm by myself, I tend to be low-energy. You might be exactly the opposite.
It helps that I have the most amazingly wonderful roommate in the world, though. 🙂