You are NOT being a b itch! Stick to your guns!
When I was having DD1 my mum said she will be at the hossy whilst I am in labour (I was in melb - 2hrs away- with DS) and I said NO you won;t be, it will be me & DH no one else, she said you can't stopme , I said yes I can when I don;t call you to tell you I am in labour!
She then said she will over as soon as bubs is born but as I had had a traumatic birth with DS and he was taken beofre I could hold & feed him etc I wanted some time with bubs as it was a whole new experience for me and I wanted to concentrate on feeding, I ended up tealling her that if she did not respect my wishes I would simply not ring her when bubs is born and she can find out when I am ready for visitors!
She got the hint and as it turned out she was looking after DS anyway but I still think she was put out as we asked her to bring him to the hossy then just give us 20mins alone with him and bubs before actually visiting!
They have a whole lifetime to meet and bond with bubs, one day will not hurt, I would also be telling the nurses that you DO NOT want visitors and if you do decide to let them in ask a nurse to come and ask them to leave afetr a certain amount of time.
Good Luck and remeber this is YOUR baby, you can decide who visits and when!