Can't speak specifically to Bliss Out.
Lifestyle clubs that organize gang bangs often already have a few regular females that are interested in GB events. They will often try to set it up so that it is convenient for many of these females/couples to attend. Just like they do with other events that have special attendees (like BDSM).
As a single male the first rule is going to be: BE CLEAN. I mean super clean, especially your breath. After that be somewhat personable and not sheepish. At least not for a GB. It would help a lot more if you were a club regular, as that way people get to know you and you are more likely to be invited based on your personality.
As for looks, everyone likes different things, and people in the lifestyle come from all types. Clubs tend to cater towards different crowds though, Bliss just is one of the few that caters towards foreigners.
Paid companions, they may get you in the door, but if they are not playing, you are just another single guy. And if they appear to be extremely attractive and you are not, and they are not playing, everyone will sense that there is a reason why. I've known guys to bring escorts to lifestyle events, and if the escort is playing it can be pulled off well, but if not, you are more likely to be further ostracized.