As you hopefully know, we are really talking about "fenders" here, not
"bumpers". It is common to hang fenders from thngs other than cleats,
such as grab rails and bow rails. That will usually get the job done
but you could also install a new cleat or two if needed, usually a
small one will do. The attachment/adjusting device you are looking
for is called a knot, usually a clove hitch or double half hitch.
None of the commercially available replacements work as well or last
as long, and you'll have the satisfaction of learning a new skill.

http://www.cptdave.com/clove-hitch.html

http://www.cptdave.com/double-half-hitch.html

My personal preference is to tie on with a clove hitch, adjust the
length while knot still loose, and then lock it with a double half
hitch.


Good advice about the knots. I believe the same device can be called both a
"bumper" and a "fender" depending on how it's used. An inflated plastic object
suspended from a boat is a fender. Permanently secured to a dock, it can be
called a bumper.

Even so, I've seen some pretty salty guys call fenders "bumpers" and nobody
minds too much.

Fender/bumper may be similar to rope/line. When you know absolutely nothing
about boating terminology, you are likely to use the term "rope" for all hemp,
nylon, or polyester cordage on a boat. When you learn so little that you think
you know it all, you might fall into the school that is horrified to ever hear
the term "rope" used on a boat, and be quick to offer the corrected term
"line." When you learn enough to realize you don't know anywhere nearly
everything, you discover that there are proper and improper uses for the term
"rope" on a boat, and in cases where the term is properly used substituting
"line" is
ridiculous.

Once again, outside the yacht club circuit people are mainly concerned that the
meaning of your communication is clear.
Nobody laughs at a guy who crabs in the Gulf of Alaska in the wintertime
because he says "rope" where "line" might be better or calls a fender a
"bumper."

Sailing terminology of course is another matter. I know a guy who loves to tell
a sailboat racing story. Seems that he invited a powerboating friend to observe
the race from the committee boat. After the fleet rounded a mark, the sailor
asked the stinkpotter what he thought about sail racing. The stinkpotter
answered, "I've been paying careful attention to the commands shouted at the
crews as they round the mark, and I'm convinced there are only two sails
employed on these boats. What I need to know is, which is the 'f***ing sail'
that needs to come down and which is the 'godd*m sail' that needs to go up?"