I would first repair and stabilize the holes in the fabric. You can purchase a small quantity of interfacing, which is a stabilizer. You have a choice of sew-in or iron-on. If at all possible, I would choose iron-on ---- but you've got to be certain that your fabric can take the high heat of the iron. If it's nylon fabric, you can't do iron-on. If it's cotton, you can do iron-on. If you're unsure, take the bags with you to the fabric store. Someone there can look at your fabric and tell you what you can use.
Cut a piece of interfacing to extend about 1" (all around) past the area to be reinforced. Turn the bag wrong side out, and apply the interfacing on the inside, so that it won't be visible.
That reinforces your fabric. Now you can figure out what sort of holes you want for the string.
Option 1 -- If you have a sewing machine, you can make buttonholes in the re-inforced area.
Option 2 -- Grommets are good, too. If you have a nice-size fabric store nearby, you can probably get what you need there. In addition to the grommets, you will have to purchase the special grommet tools. The grommet cutter cuts the perfectly-sized round hole. Then you put the 2 pieces of the grommet in place -- There is a male piece and a female piece. Male piece on bottom -- then the fabric, then the female piece. Then you must have the grommet setter -- you use this with a hammer to permanently set the 2 pieces together, gripping the fabric between. Just my personal opinion, but I would be hesitant to use the grommets or eyelets that are sold with scrapbooking supplies. They are not made to be used on fabric, and they are not intended to support any sort of weight. I would use grommets intended for fabric.
Option 3 -- I saw this on the Joann fabrics website. If you can locate it, it would be much simpler than inserting your own grommets.
http://www.joann.com/joann/catalog.jsp?CATID=cat3412&PRODID=prd56031
It's a 1" wide ribbon with the grommets already in place. (The price on the website is for an entire roll.) If you can find a store where you can buy this by the yard, then you just need one piece with 2 grommets for each corner of each bag. Sew the piece to each corner, and thread the string through --- no need to make holes in the fabric.
Option 4 -- Sew small rings at each corner. Be sure to use strong thread, take plenty of stitches, and sew it onto the stablized portion of the fabric. After stitching and knotting the fabric, place a small dot of white glue on the knot. It will dry clear, and it will prevent the knot from slipping. You can use Roman Shade rings, available at the fabric store.
If you have a JoAnn or a Hancock's or some other fabric store, you should be able to find all of these supplies there.