Your son is very young and I wouldn't bathe him that late. When my son was a newborn, I bathed him every other day in the late afternoon or early evening. Ten o' clock at night just seems very late, both for him and for you too. I am sure as little as he is that he is not sleeping through the night, but ten still seems late for a bath. What time do you put him down for the evening?
I usually give him a bath around 8, nurse and put him in his crib, like bedtime routine. But it seems like he's not ready for bed, because he would fall asleep right after the bedtime routine but keeps waking up every half hour and cry until around 11 then he would sleep straight to 11a.m. So I was thinking If I do the bedtime routine at 10 then maybe he would sleep straight to morning without waking up every half hour.