While she was snip snipping my big hair into a long bob or shlob - think sh-loppy +bob - my lovely hairdresser said she wasn't looking forward to going new bikini shopping before her holiday. You know how she felt - the ghastly changing room lighting, the heat, the regrets, the pastiness, the too big/too small combinations that someone else has decided your body is.
So, this is a possible solution. You need to know the gap you're trying to bridge first.
When you've turned the tube the right way, iron it. Make sure the seam goes either top or bottom on both, so that it's neat.
Bikini tops often come with strips of clingy, grippy rubber to hold the bra top up and stop it from slipping down as you roll over, adjust your sunnies or actually play beach volleyball. This grippy strip will grip your machine foot or feed dogs in an insane way. Add a layer of paper (photocopy or baking - I used a scrap of pattern paper). Ta-daah. Doesn't stick.
I used fold over elastic to hide my white stitching. I secured it with hand stitching. This shouldn't take too long - about an hour of finding the right fabric, sewing and finishing.