I think if bubby is fairly clean then waiting till you get home would be fine too! I think with DD I gave her a bath on day 2 but only really because she had a big crusty, bloody patch stuck in her hair right on top of her head! Not very appealing to our visitors in hossy
I had a shower in the birth suite after I was all sewn up, and after DD had her first feed (maybe around 2 hours after she was born). I did use a yummy shower gel because I felt and looked pretty gunky! But I do think waiting until bubs has latched on to the boob for the first time before using nice smelly bath products, is definitely the way to go. We were told the nipple gives off the same scent as amniotic fluid so that bub knows where to latch on to in that early time. Must be a real comfort for a newborn to smell that scent which would be so familar to them, especially after they have just entered the world which is so different to the womb.

Awww, makes me think of all that beautiful, soft newborn skin that is just so kissable!!