Our pediatrician suggested 15 months, that it was no rush at 1 yr to switch.
Cold turkey does sound harsh, and it would probably be a tough few days or week, but probably works... Most parents don't want a cranky baby though! It's up to you-- you and hubby/daddy can decide a timeline and ease off bottles on your own schedule. I'm sure anywhere from 2-3 weeks to 2-3 months is reasonable.
We slowly took one bottle away at a time, and now my 15 month old just had her last (night-time) bottle last week. To ease off the last one, we reduced the amount every week or two from 6oz, to 4oz, to 2oz and it took us a month to do it.
I always give/offer her a cup of milk or water with every meal. Usually it's in a sippy cup, but I'm also trying to teach her how to use a regular cup (which I think is tougher on mommy to do!). I also let her wander around with one (but my mom disagrees with me on this one).
Try several different types of sippy cups, as you may find one is better or easier to use. I found the Playtex one was difficult at first for her to suck on (we started using it a 10mo old) and I removed 1/2 the valve, but now I like it w/valve b/c it doesn't spill much. Target sells a Munchkin cup w/silicone top, kinda like Nuby has and I loved that one until my daughter discovered sticking her finger in the top and the "no spill" feature is broken now. I also tried the Avent tops that you can use on a regular bottle, but those were a flop--hard to suck on, difficult to clean, and confused my baby b/c it still is on a bottle. I actually like the cheap, "take n toss" cups too.
Good luck, and don't stress over it!
P.S. no cups/bottles in bed. And only water after brushing teeth at night--a sippy cup of milk has the same effect as a bottle as far as the sucking action and sticking to back of teeth.