Well, smoke comes from 3 sources: condensation, fuel, oil.
Condensation is white, burns off in a couple minutes, happens every so often.
Fuel is black, sometimes confused with blue in certain light. Too rich a/f mix OR fuel not burning completely. A check of the spark plugs can determine this.
Oil is blue, it has a distinct smell. If you miss it, fire the bike up with the exhaust facing into the garage and run it a couple minutes and you should smell it!
Oil burning is USUALLY 1 of 2 things. Oil leaking passed valves or rings. A spark plug check can also help determine if it is oil that is being burned.
I would rule out condensation, so that leaves oil or fuel. Your plugs would tell you which 1 and either leaves tell-tale signs on the plugs.
Once you have determined which it is, then a direction can be decided.
The ride IS the adventure. The destination is just to get gas!