Worth spending the money for a good one and making sure it fits correctly. My strapless bra, it’s an OnGossamer doesn’t slip around. There are many popular brands that should stay in place. I personally think Victoria Secret bras are horrible, but they might be better now than years past. I don’t know what brand yours is.
Regular bras are more comfortable, no question, and I try to buy shirts and dresses that allow me to wear a regular bra. When I had my accident I couldn’t wear a regular bra for 6 weeks. Mostly I was braless, but towards the end of the 6 weeks sometimes I wore a strapless bra when out in public. The only thing very annoying is it only looked good under a few of my shirts.
Not to get off track, but my guess is you might be wearing your bras too big around the back. Possibly all your bras. Do you have trouble with your straps falling down on regular bras?
An alternative to strapless bras is get the stickies that basically adhere to your breasts. I’m allergic to them, so I can’t use them. I have worn them and they work well for A-C cups. After using them a couple times I realized my redness from them wasn’t typical. I have trouble with Bandaids and other adhesives and latex, many people don’t though.
Another thing to consider is a bra with a bodice or bustier. It should feel more stationary on your body.