Personally I don't feel it's a good idea to take a gas powered motorized bicycle into your house. A garage is a little different in that they are usually, or should be, built to code with the electrical elevated off the floor. A garage is designed to contain a fire to some degree but your house isn't.
If gas fumes are as strong as you say they have no business inside your house. That's asking for trouble.
Even with the fuel petcock turned off and the carb drained, the fuel tank is vented to the atmosphere. That means fumes can/will escape. Not good.
Tom