Try shipwreckbeads.com a great source for antique and vintage NOS glass beads. I searched for "tube beads" and some came up. ("short tube beads" was too specific, didn't work.) Their prices are terrific, too.
I am not familiar with what “basket beads” are - and- the picture does not show the size.
In uk we generally use the term “tile bead” for regular moulded opaque Prosser beads - cylindrical with large holes, they are as wide as they are long, and were constructed into patterned table mats in various colourful hues ...
I think there was a beadwork trend (in England?) of making baskets from tubular drawn glass beads ca. 100 years ago, or even longer. I've seen photos—though I cannot place my hands on one at the moment. So I know these things were made, without knowing much more information about them.
I wonder if these were the "basket beads" being referred to (?).
I suppose Carole Morris might know more.
Jamey