I now this maybe a silly question but I notice when I got off my new to me Big bear I saw gas dripping from a tube hangin down at the back of the engine it obviously is some over flow but I don't think its safe any ideas when I shut the tank valve off it stops. The tube has a 6 inch opaque colored tube hanging from a black tube

 

Welcome to the forums.

Does it come from the bottom of the carb?

 

It will be the carb overflow, it is there so fuel doesn't run out of carb onto engine cases if the float needle sticks. Turn the fuel tap off, this stops you wasting fuel. I usually try running the bike until it stops with tap off. Open tap and the flush of fuel may dislodge any grit stuck to the needle, if that doesn't work you have to remove the float needle and clean it and seat. If that doesn't work, fit a new needle and check the float isn't holed. If that doesn't work you must have a lot of dirt in the tank. I usually go for an in line filter, but the paper element type tends to "air lock" if you run out of fuel.