We go to the library once a week and we check out a lot of books. Our old library bag was falling apart and was not nearly big enough. Keeping 3 precocious readers in books is a hard feat. Add to that the picture books we take home for the 4 year old and our bag gets crammed every week. On a side note, one thing I've found about picking out chapter books for my 14, 12 and 9 year olds is to pick a variety (they really can't come to the library with me every week) and then not expect them to read all of the books I bring home, but at least they have a choice. If there is a book that is really good, but they don't want to open it (because mom recommended it of course), I check it out a bunch of times, and eventually they'll pick it up.
As for the bag, just a simple tote bag, lined, with a pocket for the library cards and lists of books to check out. The letters I put on using the freezer paper method. Pretty simple. Not much to it and now we have a new library bag.