If this bike is rated up to 20 miles per charge, the dealer should have told you this range was only achievable under "ideal conditions". Ideal conditions would be flat terrain, no wind, rider weight of 150lbs and constant pedaling. Since most people won't pedal constantly and conditions aren't always perfect, the average rider will usually get 8-12 miles. We never tell our customers to expect the max rated distance provided by the manufacturer. It's never accurate...
A good rule of thumb (if you don't plan on pedaling much), is to expect a range close to the AH rating of the battery. In this case, a 36V/10AH battery should get you about 10 miles. Sounds like that's what you're getting...
Battery meters included on most bikes aren't very accurate. After a few rides you should be able to figure out when to expect power to run out (either based on distance -- or on how the lights change)...