Answered on September 11,2019
When you bring your UP registered bike to Bangalore, you need to change the address in RC book within 30 days of reaching Bangalore. You have to pay road tax in Bangalore (Road Tax Calculator) as well.
As per Motor Vehicle Act, a Vehicle is not permitted to ply with other state registration mark beyond 11 months from the date of migration. So you should apply and obtain the Karnataka Registration mark before that period.
Detailed procedure is provided in the link below.