I was faced with this dilemma recently, and adding to the problem was that the bottle--a humming bird feeder--is square rather than round, making it necessary to have a brush with sideways bristles.
The sideways bristles, of course, immediately suggested a toothbrush, which I easily obtained. But it was too short to reach the bottom of the bottle.
Solution: A quick trip to the tool bench in the garage. I drilled a hole in the end of the toothbrush and screwed about a quarter of an inch of a three-inch drywall screw into the end. This lengthened the brush enough to clean the entire bottle.
Note that you can use many different kinds and lengths of screws--or even a piece of screw rod--to make a brush with whatever length you require. Home Depot and Lowe's both carry the screws you might need.