Hi David!
The way we try and get out little furballs into the baskets is by treats!
We also leave the basket out a day or so before we have to take them anywhere and leave the doors or tops off them so they can go in and out!
Squeak hates going in no matter what so we have got a wire basket and has its lid on top so we just pop her in and shut the lid quick!! Bubble is just easy...we just pick her up and she is kind of resigned to the fact that she may as well go in....phew...good girl!!!

Good luck!