Best one - take the case outside, burn / dump in trash, get new case.
Remove strings (I'd suggest new ones as the funk will be trapped deep in the windings, and being me, I'd suggest tapewounds) and completely clean the bass, leaving it outside in the sunshine whenever possible. Do not associate it with a case until it and the case are both dog-stench free. Take some lemon oil to the fretboard, you'll be amazed at how much crud comes off most basses - it's much easier to do a good job with the strings off. What you clean the rest of the bass with depends a lot on what the bass is finished with - typical polyurethane finish is tough, so most household cleaners are fine, nitrocellulose is fussier and someone other than me could better advise about that.
Down several notches - place open case outside in the sunshine. Vacuum the heck out of it, dump in a pound of cheap ground coffee, close it, shake the case all around, leave it for several days, vacuum the heck out of it, leave it in the sun some more. Bring in, put a large amount of of baking soda in a shallow open box or on a sheet of newspaper (you want maximum exposure, not just ripping the top off the box it comes in) close and leave for a few days, open and dump the baking soda, case back in the sunshine. Baking soda is more prone (than coffee grounds) to get stuck and be hard to vacuum out if in direct contact with the "case fur."
Try some "pet odor eliminator" spray from a pet store or the pet aisle of a box store.
Still bad, move to cedar shavings, or rent a steam cleaner with a hose/small head intended for doing furniture (rather than just being set up for floors) and do that early in the morning on a day when you can set it out to dry.