Unofficially official or unofficial and dating?

So, I have been seeing this guy for 2 months. BOTH of us have agreed we wanna take things slow and let them progress since we both have just recently gotten out of ugly relationships. So, we pretty much are unofficially official, he takes me everywhere with him, family bbqs, parties etc. He never corrects anyone when they call me his gf. He gives me roses, shows public affection, asks my opinion about everything before he makes a decision. However, he continuously makes it clear that hes single and likes to party. ok I have no problem with that...however, Im starting to get asked out a lot and idk what to tell these guys. I dont want my "potential" to think that I wanna rush the relationship cuz i dont (i like where we are) and I dont want him to think that I wanna sleep around or see other people (cuz in all honestly I am only interested in him) BUT i am single..and shouldnt I be dating? especially if hes always saying hes single, no one can tie him down, he likes to party crap...shouldnt i be free to date? Or is the fact that he acts like a bf we are just unofficially together the top of the cake and no I shouldnt date? Ps..that I am aware of, he is not seeing anyone other than me.