If you are going under general anaesthesia, you won't be able to ride home, and they probably won't even let you try. Even though it's a relatively minor surgery, it's common nowadays to go under general. If it's just local anaesthesia with no sedative or anything, you can probably drive home, but you probably won't want to bike.
As for the next day, when I had mine done, I wouldn't have wanted to commute with all the vicodin I was taking. That was before I started seriously riding, so I wasn't in any kind of physical shape. The pain was pretty bad for a few days (I had all 4 pulled, so yours probably won't be as bad).
I guess it's all up to personal ability whether or not you'll be able to ride. I can say if it were me, I would lay off for a day or two. One thing to keep in mind is you cant suck on a water bottle or you risk a dry socket. Also your jaw will stiffen up and you won't be able to eat normal food. For the first few days after mine, I wasn't eating enough calories to do anything strenuous. I don't know how hard your commute is, but mine is quite hilly and takes some extra calories. I remember trying to eat pizza a few days after the surgery, and the soft fluffy crust was like chewing rubber and I couldn't finish the whole slice.