Trying to figure out how to get my PCs from the forgotten realms to my adapted world (from another RPG). Reason being the world I adapted has different races than D&D and I didn’t want to force the players into a corner. My first thought was to have the PCs approached by a mysterious person from the adapted world in a tavern and offer a quest without giving them all th details (like they will be trapped in my world until they complete the quest). If the players refuse the NPC will magically transport them anyway and they’ll wake up in my adapted world the next morning. 

Anyone think that’s a bad idea, or have a bette one?

there is an old video  game, "Strahd's Possession" where the heros/you get transported to ravenloft, in fact from forgotten realms. 

you can you tube one of the "let's play" videos but essentially you chase an assailant into the wilderness and when you pick up a specific item  off the corpse, the mists come and you find yourself in an unfamiliar land.

If you want your players to go willingly, give them a reason to go. Just give them a description of a strange looking man...beast...thing... Have this NPC ask them for help, that right there is generally enough for the players to get on board with anything you throw at them. They'll walk, all smiles and curiosity, right into the maw of the devil if you make them curious enough. If they're reluctant, there's usually a price that'll motivate them, from money, to items, to the "my puppy has necrotic laryngitis" bit, stack on some decent incentives and they'll go along with it.

If you have to make them show up in the strange new place, go for it. The caveat here is: don't make this a habit! Players really, really, really dislike having something happen to their characters that they have no control over. However, throwing them the occasional curve-ball of "The gods are going to turn your lives upside down today" can be interesting.

Thank you @DMThac0 that’s good insight. I think I’m going to start off the PCs in a tavern somewhere in Waterdeep and have them be approach by someone that looks like a Firbolg with a plea for help to save their forest. If the PCs agree their reward will be a magical sword that can be found in the forest on their journey. That should entice level one PCs. 

@Gigaflop thanks if my plan fails I can use something like that as a backup.. like the players didn’t agree to aid the NPC, so the NPC leaves a strain object in their room and it transports them when they find and touch it.

Every time. Want my pcs in a different world entirely it's time to employ the wierd swirly thing, laying alseep at night wierd swirly thing comes barreling down the road whisks you all up and suddenly you feel yourselves falling land in a heap, someone casts a spell suddenly it goes wrong wierd swirly thing happens everyone gets sucked through, or even once walking down a road you see a wooden door and doorframe such as you'd find on the front of a house, the rogue opens the door and everyone within 30 metres gets sucked through the wierd swirly thing, the spell backfiring one was particularly fun as it pulled the opponent's through too, so they could continue their fight as soon as they got up, another time after being pulled through. Had drawn up a map of a farm and split it into 20 sections roll d20 to see which square you land in.

One up a tree, one crashed through the roof the privy, one in the pig pen, one on the roof of the barn, and an irate farmer who no one can understand waving a pitchfork and shouting at them, you can have great fun with the wierd swirly thing