I think you will find that there is an intercity service but that it goes via Rotorua which of course adds a couple of hours to the journey.
Have a look at
which lists a number of transport operators in the Bay of Plenty
There is also a bus company called Hopper Bus - baybus service for Tauranga to Whakatane www.baybus.co.nz.
Is there a reason for stopping off in Whakatane, rather than travel from Tauranga to Gisborne directly?