Taranaki referee Paul Williams awarded the Magpies their first penalty in the 34th minute when West was obstructed after putting a kick through and he succeeded with the penalty from in front of the posts and the hosts led 10-7 at halftime.
Superb continuity from the Steamers saw centre Lalakai Foketi score in the 42nd minute. The visitors had their third try eight minutes later when substitute prop Solomona Sakalia scored from a lineout drive.
Hollinshead slotted the conversion from wide out and the Steamers led 19-10. The Magpies dodged a bullet when substitute hooker and captain Ash Dixon successfully appealed for an obstruction call after Steamers No 8 Joe Tupe scored in the 63rd minute.
Bay of Plenty had their bonus point try in the 72nd minute when Williams awarded a suspect penalty try. Hollinshead added the conversion.
The Magpies replied with a try to centre Jonah Lowe which West converted three minutes later. Another Lowe try, which West converted in the 78th minute had the Magpies trailing 26-24 going into the final two minutes.
There wasn't one of those Houdini comeback like the Magpies produced in 2015 but this was 2016 and this wasn't the Magpies year.
Scorers:
Hawke's Bay 24 (Jonah Lowe 2, Brad Weber tries; Ihaia West pen, 3 cons), Bay of Plenty 26 (Te Aihe Toma, Lalakai Foketi, Solomona Sakalia, penalty try tries; Dan Hollinshead 3 cons ). HT: 10-7.