It's completely normal for your airlock to only bubble for a few days. However, you shouldn't use your airlock as a gauge of fermentation. Sometimes it occurs overnight while your sleeping or the gas is escaping out of the lid and doesn't need to escape through the airlock so while it is a sign of fermentation, don't rely on it.
You are able to leave your beer in the fermenter for weeks. Some people on this forum prefer to leave their beer in their fermenter for a number of weeks to let it age while others bottle the beer right after the fermentation is done.
It's all personal preference.
Use your hydrometer readings to determine when the fermentation is done. If you're antsy because it's your first brew, go ahead and bottle. If you feel like waiting an extra week to let it age, go ahead and do that.
Either way I'm sure it will turn out fine and you'll be stoked about your new hobby!