It sounds like something electrical, bikes are prone to this with all the semi-exposed electrical contacts.
I would start with the battery trace where the wires go to, and spray the contacts and connections good with some wd-40, then follow as many wires as you can and contacts and fuses, and even spark plug wires, trust me something electrical got wet , and it is just a matter of finding it.
This happened one time to my old Honda, and we push started it with my friends motorcycle, tied a rope from back of his bike to front of mine, I put it in 2nd gear, put in my clutch, when he took off slowly and we got up to about 5 miles an hour I released my clutch and after about of 50 ft. of spitting and spopping she started...