There is a bus from phuntsoling to Thimphu which is 6 hours apart. Else you can opt for a cab. Bus cost ranges between 300rs to 500rs and there is a direct bus. Cost if cab comes between 2k to 2.5k and reaching time will be much earlier. Regarding entry permit, if you have your passport permit is not needed. Regarding bike permit you need to have a valid DL plus bike documents. Else for permit entry passport will do.