stockinette edges curling...
 

So I am BRAND new to knitting. I actually am just practicing to knit and purl. I decided to try and turn my practice swatch into a bib, but now that I've done about 15 rows I've learned that stockinette edges curl.

So, my original plan was to add a crochet edging around the bib, would that help it lay flat or do I just need to forget it?

I think a crochet edge would help, sure. You can also look at the sticky at the top of this page regarding stockinette curling and it will give you some other ideas to control curling, borders to put on for your next project.

I just finished a sweater in stockinette stitch with a crocheted edging and it lays flat. The pattern called for 1 row of single crochet, and 1 row of single crochet with picots (sc in next sc, ch3, sl in top of sc, sc in next sc) and repeat.

Stockinette curling is the nature of the beast. At the top of the page is a sticky post for just this issue so do check that out.