Hi!
It does sound like you might have got water in something and fused it - at least, it's a bit of a coincidence. Although, I don't see how an ordinary wash could have got into the electrics under the bonnet unless the bonnet was open, or you used a jetwash and water was forced in where it shouldn't be.
Check you don't have a fluid leak somewhere in the engine itself that's somehow sprayed or leaked leaked into the electrics. Has the bonnet seal failed and water is getting underneath? Your little screenwash hose and the coolant hoses aren't leaking or spraying anything across the engine?
Before you think of changing the alternator, double check the battery, charge it up out of the car, and make sure it's taking/holding charge properly, and isn't faulty / hasn't been damaged in any way. Check also that your battery cables are OK and the connections are clean and fit the battery posts tightly. Then you can be sure the issue is elsewhere.
Try to find out, too, where the burning smell came from - if you had smoke (and it was definitely smoke, and not steam or water vaporising off a hot surface), can you see if anything actually burned out, is there any melted plastic or rubber? If something is damaged and shorting, and a particular sytem keeps working after the ignition is off, that could also be a battery drain.
If you do determine that it's the alternator, get the part number off it, but I think you will need the chunkier version. The Mazda EPC suggests the V6 alternator part no. is K80118300C, and online that's bringing up equivalent parts at 90 amp. I have a 45ah battery in my V6 and it's doing fine.
A quick time-saver: when you remove the alternator belt, note how many turns (half or quarter) you make on the tensioner screw. Then when you replace the belt, tighten the tensioner back up by exactly that number of turns. It might still need a bit of adjustment as the new belt won't be stretched, but it means you'll have it roughly right and won't have to spend hours trying to get the tension even into the right ballpark. It's quite a fine-tuned thing: I had both belts off on several occasions when replacing the PAS, and just a quarter turn too much or too little produces either a horrible rattle or that awful squeal!
While the alternator belt is off, do a visual on the pulleys, check all the nuts are tight but the small guide pulley is still turning freely. While all that's off, you might as well do a quick visual inspection of the other belts as well, or as much as you can as they're in situ, make sure there are no obvious cracks etc.
S