@toileandtrouble I'm pleased you're going to give it a try too. If you go for fold-over elastic it's straight forward but if you like the lycra binding it's not as tricky as you might fear.
A 1" strip is good and wide for binding around a 1/4" seam allowance with a nice bit to trim close to the stitching afterwards. It's a double fold at the front but just sewn flat at the back for less bulk and fiddle factor. The top edges are easy because both ends are open and I stitched it all in the ditch from the front to catch the back of the binding. Only the sides with straps are more a tiny bit more fiddly.
You can't judge strap length from the fold-over elastic measurement quoted in the pattern so once I'd bound the front and back pieces I actually pinned the swimsuit onto the doll (pain-free under hypnosis naturally) to estimate the length for the straps so I could just add that to the length of the suit underarm sections. I think reduced it to 85% of the full measurement so it would keep it from stretching out too much with all the taking off and on.
The straps were very co-operative wanting to follow the same folds as the binding. My curved nail scissors worked really well in trimming the excess close to the stitching.
There was a bit of gap at the back of the strap transition but I did pop a few handstitches there afterwards.