You can buy webbing straps to attach the stirrups to the girth but I really dont like the idea. Only time in the saddle will help you with your balance. Good luck
As much as i Hated/Hate it I did lots of bareback work and no stirrups and omg it helped so much my balance is amzing now even if i do say so myself! I would certinly give it a shot, even if you are one of those people who hate it(like me, i literally had to force myself to do it) But certinly was worth it
Attaching the stirrups to the girth won't help you be more secure in the saddle, as others have said, try to get some lunge lessons on a safe horse, it will help a lot. You need to have the confidence to relax and move with the horse and not grip too tight. Don't let anyone frighten you by lunging on something stupid.
I wouldn't tie the stirrups to the girth, i'd get yourself some lessons and do lots of stirrupless canter work - would be a safer alternative and it will help you more long term as will improve your balance
Thanks I do hate no stirrups/bareback as it petrifies me! But like you said it's best to make yourself do it! Luckily I have a very kind horse and a good RI so here goes!