that sounds exactly like my experiences (minus the bathtub thing, though they have other things that make us laugh). Willow hated all cats, until we brought Buffy home, as a 4 week old. Willow hissed once, and we shut her away in a room and let Buffy roam and explore her new home. During the course of the next week, Buffy and Willow learned that they weren't going to get threatened by the other. By the end of the first week, they finally started to play together. Well, Buffy was playing in a basket, when she spotted a cheesie and started to eat it. Willow, who had been following Buffy around the house for the past week but would run if Buffy came towards her, came forward to see what the crunching sounds were coming from. She saw, and then suddenly she flipped onto her back, and started pawing at Buffy's tail, which was hanging out of the basket. Buffy didn't notice at first, but when she did, she flew backwards and hissed (sounded like a gasp at her young age). She then growled, and then spent the next 10 minutes just growling to herself, fascinated by the new sounds. She had to be sent to a room to calm down and nap, since she was starting to get cranky.
The next time they met, they learned that they weren't going to hurt each other, and over the next week, they started getting really close. A maximum of 2 weeks after they first met, Buffy and Willow were grooming each other, playing with each other, fighting with each other, sharing food bowls with each other, etc. Willow turned into a mom for Buffy, since Buffy's momma died (same with the siblings, and she was going to be put down the next day). Nowadays, they still sleep together and groom each other, but it's waned a little bit. I think its because Buffy is a HUGE bundle of energy, and Willow is getting tired from the constant leaps and jumps, tired of Buffy trying to get her to play at practically all hours of the day. The main time Willow will get hyper and play with Buffy is in the mornings, when my parents are getting ready for work, and at night when people are getting ready for bed, and any other time people are rushing around, ready to do something.