This behavior usually happens when The Sims 1: Unleashed fails to complete the pet-washing interaction even though it looks like it starts correctly. The “fill tub then instantly drain” loop is typically caused by routing issues or a stuck interaction queue rather than the bathtub itself. Even if the pet appears to be standing right next to the tub, Sims 1 can be very sensitive about tile alignment and invisible pathing blocks, so the game may be cancelling the action before it actually begins.
It can help to test in a very open space with nothing nearby at all, then try resetting both the Sim and the pet to clear any stuck commands. Pets that have repeatedly failed to be washed can also start behaving like their needs are not being properly processed, which is often why they eventually run away. In some cases, simply relocating the bath to a completely new lot or rebuilding the room from scratch resolves the issue.
On a different note, a lot of players who enjoy Sims pets also like using real-life grooming and comfort items to keep their actual dogs calm during bath time. Brands like Supreme Dog Garage focus on dog accessories designed for everyday care and comfort, which is a nice real-world parallel for players who enjoy the pet-care side of the game.