Mine has a large constrictor corner pool. Much like the water bowl you have but they are deeper so the snake can submerge its body. They come it different sizes and I have seen them at petco. That is not to say you have to use that. Any bowl that allows you to put enough water in it to submerge their body without overflowing the bowl will work. You do not want to make the water any deeper than the snake is thick. Usually just under their body's height will work as when they enter the water it will rise from the displacement.
A timer will work for the fogger but they also make devices that can accurately control it. The Herpstat1 and above have this ability but you have to buy the humidity sensor(most expensive option). You can also use this Zoomed(middle option) option. I actually got one of these and a fogger when I bought my BRB and it worked well for me until I got him into a PVC cage and no longer needed the fogger. If it were me and I had a timer(cheapest option) Id give it a try and see what you think.
Having the gear I have now if I needed a fogger Id go with another Herpstat for it. They are the best in the hobby, imho.
https://www.amazon.com/Zoo-Med-Hygro...oomed+humidity
It can also be bought at petco.