We don't have a dishwasher (non-human

) either, so brushes are quite useful. Surely, you can find something that will do the job.

(click for larger image)
Although mine were obtained elsewhere, brushes such as these I have seen in science stores.
If hot soapy water does not work, you could try a mild alkali. A quick squirt of oven cleaner (with appropriate precaution and ventilation) into the bottle may help.
American Science & Surplus
5316 N. Milwaukee Avenue
Chicago, IL
773-763-0313
33W361 Route 38, 1/4 mile east of Kirk Road
Geneva/West Chicago, Illinois
630-232-2882
http://www.sciplus.com/stores.cfm