It depends on what it's made of. Most beanbag chairs have double zippers for this sort of problem. If it's a washable fabric, get yourself a big bucket or box or garbage can, empty out the contents of the beanbag into it and toss the cover in the wash. If it's not a washable fabric, empty it out, and sponge it down inside and out, then sprinkle with baking soda and hang it dry, sunning it if you get a sunny day.
I would also take the "beans" and toss some baking soda with them. Let them dry out for a couple days, and then give them the sniff test. If they smell like pee, take a handful and try washing them. Do they absorb the water, or can you just give them a wash? If they absorb the water, you may be looking at replacing them (since they absorbed the pee). If they don't absorb it, rinse them really well, maybe with some vinegar, then lay them out to dry (lids of rubbermaid tubs, baking sheets, whatever you have that's large and shallow). This is liable to take a couple days unless you can get them near a heat source (I'd have to do it in the basement or risk the cats knocking them over). Stir them periodically so they all dry thoroughly. Once they're dry give them another sniff test. If all's good, repack the bag and consider a vinyl cover for it until she's done PL.