That's how I get mine too. Then they keep me overnight for observation. I go in on Monday morning, we start the infusion around mid-morning, latest noon, and finish in the evening. I am allowed home the following morning.
May I ask what your living arrangements are? Do you have people to help you at home?
I try to do a thorough clean of the house and pre-cook some extra food before the rituximab because I live alone and I don't want to have that work in the days immediately after the infusion. That way, I come back home and spend the time resting.