We use a puppy pee pad, folded to just the right size and with the absorbent side out, underneath the dog's bowls in the RV when we're parked. It absorbs drips and has saved us from a bigger mess a few times when a foot accidentally knocked the bowl. While we're in motion the water bowl is placed in the sink. It doesn't seem to slide around or slosh, but it's a small bowl for a small dog. Might not work for a larger bowl.
FWIW--our dog doesn't use pee pads, but we find them to be extremely useful for many things in the RV. We've used them on campground picnic tables while cutting a melon, as disposable rugs/shoe holders when it's wet/muddy, a couple of times when we thought something was leaking under the RV a puppy pad was just right to place beneath the suspect area to collect evidence, etc.
Lots of options, but best is not to try feed or water while in motion. And best to use a table mat of some kind under the bowls to catch and contain any spills, which WILL happen! We have used holder for bowls, both for large dogs, that needed to be raised, and for floor-lever for much smaller dogs. This is a good option... https://www.amazon.com/UPSKY-Double-Premium-Stainless-Modeling/dp/B07LF1JLZ6?ref_=Oct_NReleaseC_2975351011_2&pf_rd_r=7CJ6PKYX1WXFYHJKAJJN&pf_rd_p=616143cd-8707-5796-9cf1-25909ccb0cb1&pf_rd_s=merchandised-search-6&pf_rd_t=101&pf_rd_i=2975351011&pf_rd_m=ATVPDKIKX0DER