NO. With a CHL, you must drive your own, fully paid (no loans, etc) car. You cannot drive/ride in any kind of transportation that is not REGISTERED in your name. That means no cars, motorcycles, bicycles, skate boards, roller skate, etc. With your CHL, you can only walk if you have proof of ownership of of your footwear provided you have the receipt of payment in your possession.
Now, yes you can drive/ride in any vehicle with your CHL as long as that mode of transportation is not restricted (i.e.; aircraft) or otherwise prohibited. You can also carry your weapon any place you want as long as it's not prohibited by law or statue mor in a place where you are told not to carry it. Bone up on your state and local law and ordinances.