Hi Bonnie,
You are traveling between two of my favorite resorts!
Disney's BoardWalk Villas is my home resort with Disney Vacation Club. I love the hustle and bustle along Disney's Boardwalk.
Bay Lake Tower at Disney's Contemporary Resort is such an amazing resort. With a sleek and modern look, and a quick walk to Magic Kingdom, it is another of my family's favorite Disney Vacation Club resorts.
You can get from Disney's BoardWalk Villas to Bay Lake Tower at Disney's Contemporary Resort a couple of different ways using Disney transportation. In these cases, you will not need a car seat. I think that the simplest way is to take a bus from Disney's BoardWalk Villas to Magic Kingdom. From there, it is only about a 10-minute walk or a quick monorail or boat ride to Bay Lake Tower at Disney's Contemporary Resort. If you are then heading back to Disney's BoardWalk, simply reverse the procedure.
Another possibility is to take a taxi. In this case, you will need to have a car seat; however, you should be able to request a taxi with a car seat. You can ask a cast member at any Disney resort hotel, typically at Bell Services or the Valet, to help you call a cab. Be sure to have them request one with a car seat. Of course a taxi will come at an extra cost; however, I have found that trips within Walt Disney World in a taxi tend to be pretty reasonable.
I hope that these thoughts are helpful for you, Bonnie. Have a wonderful time planning your magical vacation, and please do let us know if you have any further questions.