What machine? Typical sewing machines have only 1 adjustable tension bias which is usually the spool/needle side.
You might need to play with the bobbin casing tension and sew some test strips of your two fabrics.
All my machines are old "steel gear" Singers and adjusting bobbin tension is easy. If you look at the bobbin casing, you'll see a flat spring that the thread slips under. There are usually two tiny screws that hold that spring. One fastens the spring to the casing, the other is for tension. You can loosen or tighten that screw and balance stitch tension against the needle side tension perfectly if you mess with it. You'll likely have to pop the bobbin casing out of the machine to get to that screw. You want the stitch loop buried between the two pieces of cloth. If your cloth is bunching up, go with a smaller needle, dial back your thread tension, maybe reduce stitch per inch setting on some test pieces. A "walking foot" helps as well. Make sure your machine is well lubricated! 99% of machine problems is lack of oil, top and bottom bearings.

Edit.... Looking at what you just made (i like it! People pay extra for those gathers! ), have a friend hold one end of the seam, you on the other end, and GENTLY pull. You might be able to stretch it out. Don't cut your seams/stitches.... a bigger "mess" will happen over time. When I make such things, especially with slick light fabrics, I spend a lot of time on test strips to get it right before destroying the real fabric.

Edit #2...I noticed something about your seams. Notice how the gathers form "echelons" with respect to each seam? That's a feed problem, not your machine. When sewing large pieces of cloth, care must be taken to feed the fabric with both hands evenly, with plenty of slack before it gets to the presser foot/needle. Else, one side of the fabric will pull, usually the side you shove under the machine side. This takes practice but once understood becomes second nature. Sewing machines can't pull much weight, and you have a heavy piece there. Still, the piece looks functional to me.