Use a ball point needle in your machine. Using a ball point needle helps eliminate popped seams by gently pushing the fibers out of its way as it enters the fabric instead of cutting through the fiber like a regular needle would. Us a small zigzag stitch to sew your seams as it will stretch with the fabric and not pop the thread as a straight stitch seam would when stretched. Using a double needle would make the seams look like a serger on the right side of the fabric and I would'nt use it for sewing the seams.If you will do a google search for sewing on spandex swimsuit fabric, I am sure you will find more information than you will need.

I use a serger. I wouldn't even attempt it without using one. 4 way stretch puts lots of strain on seams. I'd be afraid the wearer would suddenly expose themselves.