If he can not respect you privacy, then he will *never* respect you!
Wash your hands of him.
And no your phone bill will not show any of that.  But your online
information will include all the outgoing phone numbers you have made.
So if he gets online, and sees that, your goose is cooked, because
he will ask you who this or that phone number belongs too!
I have not looked, but I think there is a option that you don't
even have to have a print out come to you in the mail.  You can
get a hard copy from the online history area, or just pay online
and check your own call infor for correctness.
In my way of thinking, you only need a hard copy when there is a
problem.  (maybe i'll go look for that option myself!)