Well if it is the early days, let it develop. There's nothing wrong with not answering texts if you are asleep!
Dating is suppose to be fun. Try to ease up on yourself.
I am bp also so I understand about the paranoia but I think maybe you are getting yourself all worked up. I know you really want this to work, but worrying about it a lot won't help things, and you may get too clingy, and that he may not like.
Try to distract yourself and do something fun while he is off, having outside interests makes a person more attractive to be around.
Excellent job on the not drinking so much!