Hi Kristopher,
Welcome to @BanjoBen 's Forum, one of the best way’s to memorize a tune is to LISTEN to it over and over till you can sing or hum it in your head. I am not a mandolin player so I can’t offer any advice on playing mando but I can tell you that beginner banjo players experience much the same sort of problems playing with others.
The first thing you gotta do, is put away the TAB at a jam session. TAB is a tool for helping you learn to play your instrument of choice when your at home on your own.
Search the Mandolin section for lessons on how to play Rhythm & Backup once you have a few patterns down in your head put away the TAB and pull up one of Ben’s Guitar or Banjo solo’s and strum along. Playing along with Ben helps prepare you for playing with others. Get to know the melody and most important the chord progression. By listening you’ll learn to anticipate chord changes.
Learning to play backup helps you to build confidence to play with others.
Now go to YouTube and search for bands playing the same tune, try playing along with each of them, you will find that few bands play the tune exactly the same. Some play it fast some play it slow, some play in a different key. What this does is exposes you to different situations and will help you build confidence when you come to play with others.
At this stage don’t worry about trying to play the melody, note for note, that will kick in when you relax and get comfortable. Once you learn a solo. put the TAB away and practice playing whilst listening to yourself. Use TablEdit in your practice sessions to help you build speed - See my link below for more info.
Keep in mind playing with others is different to playing on your own, other folk may play the same tune but will more often play it differently to the way you have learned it. Don’t be afraid to tell the folks in the group that you are a beginner. Ask them if they could play one or two tunes slowly to help you get comfortable.
One last thing if you don’t have TablEdit click on this link.