Ms. Frizzle is a Time Lord who loves the late 20th/early 21st century. The Magic School bus is her TARDIS, and she takes her schoolchildren across the cosmos having adventures. She has the setting permanently set to school bus (or perhaps it’s ‘stuck’, like the Doctor’s). Possibly she sought refuge there during the Time War, and decided her place was here with these children.

Mary Poppins is also a Time Lord, but she doesn’t have a TARDIS of her own and is stranded taking the slow path through time. She lives on earth and tends to children as a nanny to pass the time. She lives on a cloud when she isn’t nannying. Her bag contains the last of her Gallifreyan possessions and was transdimensionally engineered to be bigger on the inside, like TARDISes.