Is it possible for bash completion to cycle through the alternatives?

Bind the Tab key to the menu-complete command instead of the default complete. Put the following line in your ~/.bashrc:

bind '"\C-i": menu-complete'

or the following line in your ~/.inputrc (this will apply to all programs that use the readline library, not just bash):

"\C-i": menu-complete

In bash 4.1 and later you can also use menu-complete-backward to cycle through completions backwards. I have this in my ~/.inputrc:

"\es": menu-complete-backward
"\et": menu-complete