Re walking from the BLR airport to The Taj Bangalore

There is a new partially complete pedestrian walkway that is much shorter than the above route. As you exit the T1 terminal building, turn right and walk past the uber pickup area till you reach the signs pointing to Parking/Ola, then follow the signs to Parking/P3, this takes you to a parking structure & elevated pedestrian bridge that is next to the hotel.

There does not appear to be a way to walk from the new T2 terminal building. But there is an inter terminal shuttle, so you could take the shuttle to T1 and walk from there.