Several years back, we bought a bathroom organizer that was quite narrow. Rubbermaid brand; came in three vertical sections, but you might be able to buy just the one bottom piece which could be used as a wastebasket. I assume you've already tried discount department stores (Tar-zhay, etc.) and "organized" places ("Hold It", etc.). Maybe "Bed, Bath, and Way Beyond" or "Linens and Stuff" ???

How about something like a toilet brush stand?

here's one that's 7 inches and hangs on the inside of a cabinet door; you could just toss the wire rack, and use the trash can (no lid)

Here's

is just the teeniest bit too big for your space--how exact was your measurement?

And of course, there's the

Me. I want a lid on my bathroom wastebasket.

Rubbermaid makes some that should work.

Here is a link that might be useful: This one is 5.5 inches wide, w/ the step-on pedal at one skinny end