Join a dating site for people who are celibate? I'm sure they must exist.
I don't think it's unreasonable for dates to lead to a physical relationship - at a pace appropriate for all parties - after all, dates are not about going out with a friend, they are about going out with someone you see as potentially more than a friend. If I went out with one of my male friends, we would not be on a date; when I first started seeing man hostage, we were most definitely going on dates.