I hear you man. I went through this phase my first month of dancing. As a man you can't count on the environment being follow heavy to help you. Count on yourself, and you really need to leave your ego at the door here, or it will crush you and your dance passion.
-My first few dances I have the 3-seconds approach rule. The moment I finish a dance and I see a girl not dancing I have 3 seconds to walk over and ask her. Don't let anxiety or mental excuses cloud you. I realize that's just your ego defensive mechanism. No one likes to get rejected which is always a potential in salsa. Now it changes to 1-second rule. I just do it by reflexes.
-I second @
azzey , you need to be persistent but not harassing the girl. I lost count of how many times I danced with a girl who said no but it ended up great. A lot of times girls say no bc they are beginner "But I don't know how to dance" "Well it's about time you learn then!"
-A lot of other times girls say no bc they don't know you. This is when presentation and preparation are very important. What @
azzey said, prepare your approach and identify your "prey"

Dress nicely. DO NOT SMELL BAD. Approach with a smile and an upright body (this is a game changer for me once I discovered it) It increases my success chance significantly. Might help you too.
-ASK THE GIRLS WHO ARE WITH THEIR FRIENDS! The fact that they are with friends don't mean anything. She might even wants a break from the usual bar gossip


Not sure about your scene, but here in Paris I've found that girls love it when one of theirs is being asked by a stranger and they will even encourage her


maybe it makes for good banter afterward? If I didn't ask girls who were with friends I wouldn't have a third of the dances I had. It's also the most fun experiences. After you dance with her you can ask her other friends to dance.
-If their friends try to cockblock (or danceblock)

you but the girl looks like she wants to dance, you need to man up and speak for yourself and the girl. Don't be rude but be firm. I asked a girl who was with another guy yesterday, and he basically manhandled her away

She wrestled out of his hold to dance with me. Another time I was asking a girl and her guy friend interrupted. I look at him firmly and said "It's up to her to decide bro" then I looked at her again. She was more than happy to dance. If I didn't man up I would be doing her and myself a disservice.
-If the girl does not want to dance let her tell you that. It will be obvious like a crowbar wack on the head, you can't miss it

In that case thanks her and leave. But if she's just being hesistant convince her a bit. Use your professional charm
Oh, see if you can join some university dance club/organization/class. Usually there are lots of girls willing to dance there.