If you are planning to apply for a visa from Kathmandu, you won't be issued an individual visa but a group visa to those booked on tour. You will be charged $85 for a visa through Nepali agencies. For US nationals the fee is $142. It takes at most three days. For faster services premium facilities costing more money are available. Chinese Embassy in Nepal, main office Baluwatar, branch Hattisar, accepts visa form on weekdays from 9.45 am to 11 am.
You will be granted an individual visa if you are traveling via a flight to Chinese cities outside Tibet like Chengdu and Shanghai. If you plan to visit China after Tibet, you can fly from Kathmandu to Chengdu. The plane stops in Lhasa, and for transfer, TTB permit is not required. But, when you fly back to Lhasa, you need a TTB permit on your Chinese visa. Visa extension is not possible in Tibet, and it is recommended that you try for an extension from other regions of China like Chengdu, Xi'an, and Xinning.