pin, pin, pin. Thats about all you can do.

Pin and I lift up the front of the foot with my fingernail a little and sew slowly. Mostly I avoid stretchy fabs if I can. Good luck.

Don't know if this will work, but you may put some strips of iron on stablizer along the sides so it doesn't stretch? Give it a try on a scrap.

Always sew with the more stable fabric on top and the stretch fabric underneath.

Did you quarter the fabrics when you pinned them together. That can make a big difference to how they stitch together too as it is easy to accidently stretch while pinning.
Don't pull your fabric. Ease/guide it through the stitching process.
I learnt it the hard way as I had always pulled my cotton fabrics taut as I sewed, it doesn't work on stretch fabric.
I sew on stretch all the time now and no bubbles of stretched bits.
Good luck.

Some good suggestions here...you might also try easing up on the pressure for the presser foot...

Using a serger/lockmachine gives nice seams, but when using a sewing machine I put strips of tear-away under the seam and pin. That works well too.

I cut strips of tear-a-way and pin it on top and bottom of seam and then tear away after stitching. Works for me every time. Best of luck. Hugs, Barba

Purchase a Roller Foot for straight sewing ie hems etc & a Teflon Foot for any fancy sewing ie scallops etc. Both are low priced items, and should be available from your local Machine shops. A Serger is great for 'joining seams' ie legs, 'bag pockets' side seams etc. The roller is great for sewing in elastic as it holds everything in place whilst sewing. I have used both for many years. These do a better job than the walking foot as they are faster & far easier to use on curved areas. Type in Roller/Teflon Foot on E-bay & you will find heaps. Happy sewing, Margaret

Besides all the great tips below you could make the stitch length longer and if you can adjust your foot presser tension that will help and by all means prewash. I stitched two together at Christmas time and was surprised at the difference in size after they were washed and dried and was able to trim them to the same size.

It's been awhile so I hope I remember my details correctly. I had some iron on 'small dotted' adhesive that comes on paper and is used for applique that I put on the sturdier fleece then placed it the sturdier on the wrong side. I then placed the fleece's wrong sides together and pressed the sturdier fleece (on top) to the fluffier fleece. One of the pieces was cut an inch or so bigger so I could fold it over the smaller piece of fleece tucking under 1/4-1/2 inch to act as the binding. Then I stitched it in place with a walking foot. I hope I make sense..I have even used batting that has the same adhesive. I hope I make sense. I have been up since 4am and it is 10pm.