Do I need to glue down linoleum flooring?
There is a whole new generation of fiberglass, not vinyl, flooring that is self laying. The various manufacturers say wit will lay flat, not curl or bubble without adhesive. I have my doubts, but admit I have not used it without adhesive. The manufacturer does says that when adhesive is used, it can only be "Releasable Pressure Sensitive Adhesive", never standard vinyl sheet goods adhesive.

In a small room like you have, I'd test the no glue theory. If it doesn't work well, it's easy enough to go back and glue it down with pressure sensitive adhesive.