Is there a maximum to bash file name expansion (globbing) and if so, what is it?

There is no limit (other than available memory) to the number of files that may be expanded by a bash glob.

However when those files are passed as arguments to a command that is executed (as opposed to a shell builtin or function), then you may run into a limit of the execve() system call on some systems. On most systems, that system call has a limit on the cumulative size of the arguments and environment passed to it, and on Linux also a separate limit on the size of a single arguments.

For more details, see:

• What defines the maximum size for a command single argument?
• CP: max source files number arguments for copy utility

To work around that limit, you can use (assuming GNU xargs or compatible):

printf '%s\0' foo* | xargs -r0 rm -f

Above, since printf is built-in (in bash and most Bourne-like shells), we don't hit the execve() limit. And xargs will split the list of arguments into as many rm invocations as needed to avoid the execve() limitation.

With zsh:

autoload zargs
zargs foo* -- rm -f

With ksh93:

command -x rm -f foo*

You can see the limit for the total size of the arguments with:

getconf ARG_MAX

This is determined generally not by the shell, but by the underlying operating system according to this answer.