I started the weaning process at 1 year going from formula in a bottle to milk in a sippy cup. I switched one bottle at a time, waiting 4 days or so before moving on to switching the next bottle to a sippy cup. The last bottle to go was the bedtime bottle. Your bedtime ritual sounds similar to ours. We finished with snuggling and reading a book while he had the bottle. I can't remember if we just stopped including the bottle, or if we gave him a sippy cup with water while we read the bedtime book, but he never missed the bottle. I was nervous about his reaction, but we just continued the same routine as usual (the only thing missing was the bottle) and he never gave us any indication that he was upset about not having a bottle. It was almost too easy! This was with my 2nd baby. I had planned this weaning process with my 1st baby, but he flatly refused the bottle himself at 11.5 months, so I never had a chance to start the process. I wouldn't complain, but I was a little sad because I missed the snuggle time with the bottle and I thought I had another couple of weeks to enjoy it.:) Maybe my babies were just extra easy-going, but getting rid of the bottle was no trouble even for my 2nd baby. I think it may be easier because they're so young. It seems like it is usually older babies that I hear of having trouble getting rid of the bottle.
Just to warn you, neither of my babies drank nearly the same quantity from a sippy cup as they did from the bottle. It worried me a lot, especially with my 1st, but they seem to drink what they need. And I had to alter the usual "routine" a little and offer the sippy cup throughout the day, rather than at the same set time they used to have the bottle. Neither of my babies ever drank a full sippy cup at one sitting. They "sipped" and would only take a little at a time, so I would offer the cup throughout the day, give sips during playtime, etc.
The Nuby sippy cups worked great in the beginning because it is very much like a bottle nipple, not the hard spout that most sippy cups have. They are not great because they do leak, but that helped my babies get used to sippy cups. I believe it is Playtex who also makes a beginner's sippy cup that has a spout very similar to the hard ones, but it is slightly softer to help them make the adjustment.
I hope this helps! Good luck!