I think you have the right idea, just keep at it. Sometimes it takes a bit to get them to switch.
My DS will be one in a week and I started introducing him to cow's milk 3 weeks ago. I never really pushed it and just offered it. I did introduce him to a sippy cup (just a regular toss'n'go cup, nothing fancy) earlier though so he knows how to drink from a suppy. I started with water just so he could practice and get used to it.
All I did once he was sort of used to the sippy cup was to put milk in one cup and have water in another cup. During meals I started to put the milk cup on his tray while I served him his food. At first he'd taste it and just set it back down again, sometimes it would end up on the floor etc. I never made a big deal about it and just put it back on the tray, if it became a game I'd just put it back in the fridge and bring it back again at the next meal. At first when he refused the milk I would give him the cup with water but every week I'd wait longer and longer before offering the water to him, this week I don't offer him his water during meals at all. He's not super excited to get milk which is fine by me since he drinks and likes water and I'm not a great fan of the kids drinking milk anyway, I prefer kids drink water.
If I only offered him milk I'm sure he would be used to it by now but he likes water better. I do the same pretty much with the daycare kids too. If you keep offering it they'll get used to it. If you don't offer anything else they'll get used to the milk faster.
