God i used to sell electric bikes many moons ago.
Things to consider when buying an electric bike-
Do you want it to be Electrically assisted or do you want it to run without peddling?
How heavy? You will have the option of Lead Acid batteries (heavy and short range but cheap) or Lithium ion (lighter with better range but expensive)
Ultra Motors A2B is an interesting new one its Lithium ion with a 20 mile range however a second battery pack can be added to bring it up to 40 miles. This launched in the UK last week.
UltraMotor
Probably not as of interest to you mum is this brand new speedy number really meant as halfway between a bike and a motorcycle. Elmoto[/url]