Why am I getting passes made at me as soon as I'm in a relationship

So I talked things out with the girl I'm seeing and it turns out there were severe misunderstandings on both sides. I really liked the way we were able to handle our first conflict. And she made me promise to not hold things inside when I feel hurt and bring them up so we can talk things out as soon as they happen instead of letting resentment fester. Which is something I honestly have to work on. Well long story short we're an official couple now.


Well, since then, and especially after my performance on Saturday (lol) I've been getting random women (well not completely random, I just knew them in passing but was not friends with them) getting my number from "somewhere" and hitting me up. Asking me out to "coffee chats" and the likes. Lol. I guess asking someone to coffee is the most innocent way to ask them out on a date without it being a date. Should I deny them all or just go along and then cut them off when they're explicit? I don't want to be the "I have a girlfriend" guy that isn't capable of having any other female friend.