I did something similar - making the BF seperate from the night routine - and also started reducing the BF time and taking a sippy in, too. I'd offer the sippy first, one side, then sippy, then the other.
After a while I dropped the second side (ie, sippy, breast, sippy), and kept reducing time on the breast by a 2 minutes or so every 2-3 days.
It took about a month, all up.