I made an error earlier, when I said that the beds were brought from Mexico by Mrs. Whiting. Actually, they were brought in by a later owner (and avid antique collector), Mrs. Baker. Mr. Baker was often called "Bake" by way of a nickname, which eventually led to the naming of Bake Parkway.
Incidentally, I corrected the error thanks to
this LA Times article, which describes the park.
The park is open 9-5, Wednesday through Sunday, and is free unless you're taking a large group on the tour, in which case the tour is $2pp. But in small groups the tour is also free, and takes place at 2pm.
There's a picnic area with shade structures over it as well.