Hahahaha! Solo trivia night is part of my regular routine
Go. Definitely. If there is a host to the trivia, pal around with him/her. Tell them that your friends bailed, but you wanted to come anyway. So you are going to hang out with them a bit until you find a team to join. Being seen with the host makes your later opens really easy. Find a group you like, old ladies, dudes, mixed sets, something that makes you look social, not that you are hitting on them. Open with simple hellos or observations in passing them to and from the washroom. A bit later just go back, tell them your friends bailed and you'd like to join their team if it's ok. It's a probability thing
Now you've come in alone, hung with the event's alpha, landed with some strangers and are now laughing and smiling with new friends. The server you like has seen it all, and so has every other girl in the joint.
Don't ask her to keep you company. That will sound like "I don't have any friends, will you be my friend?" Instead, when she comes to serve you, tell to stick around and hang with your new friends. Do I need to explain how much cooler that will look? If all goes well you can use this move to bounce around all night until she gets off shift. At some point earlier in the night just ask, "when do you get off? You can join me for a bit". Servers see people socializing all the time, if you have any game, go into friend mode and this move should be and look easy and natural for you. You didn't have anyone to talk to, so you snapped your fingers and made it happen, like a Jedi.
At first, look comfortable being alone, pay attention to the game, not the environment, get a little bored, and don't game the server. If your team is chatting with a neighbouring team, then try to merge the sets under the guise of make one bigger "super team" to better the chance of winning. Really, merging sets is a godlike move that blows minds.
Warning: if you pull this off your server will likely get progressively shy and nervous toward you. Kino her when she serves you and reopen and reopen until you regain your rapport.
Sound good?