Wet bags are super easy to make. Do you want one with a drawstring closure, zipper, snaps, velcro...?
Zipper closure is my personal favorite. A simple one layer zippered wetbag is pretty quick and easy to make. You want to use a plastic zipper because metal zippers might rust under the heavy washing necessary for diapering related products.
Cut a 25"x 11" strip of PUL. Place the zipper against one short edge of the PUL, right sides facing each other and edges flush {zipper should be laying on the fabric, face against the right side of the PUL}. Stitch down. Open, lay flat, gently iron {be careful ~ too much heat can warp the PUL} and topstitch. Draw up the opposite side and repeat. Open zipper about halfway and turn the fabric so that it's wrong side facing out. Stitch down both long edges. For a wetbag that opens in the front instead of on top you can scooch the zipper down a few inches before stitching the sides. Trim the seam allowance, zipper tape and corners and then turn. Voila, done! If you want a zippered wet bag with a decorative cotton outer it gets a little more tricky, but once you've mastered sewing one with just PUL it's pretty easy to figure out. I would suggest you use some cheap fabric and a recycled zipper to make a mock up first to feel out the style and get comfortable with the sewing before using a pricier fabric like PUL, unless you're already experienced in sewing. It's pretty simple, but I like making mock ups when trying something new so that I can get comfortable with the pattern/concept before using my pricier fabrics.
If you have any questions I would be happy to clarify.
ETA: Fleece can be used for wetbags, but I personally would NOT recommend that for one that is going to be placed in a diaper bag or purse. Fleece has a frequent issue with compression wicking and I would be worried about anything wet inside the wetbag leaking out onto my clean contents in my bag. It's a semi-breathable fabric, which allows smells to leach out. The contents of a wetbag are not what I want my wallet and clean change of clothes smelling like!
