The TBBC is a great bullet. The only thing I have ever herd about them is one friend of mine could not get them to shoot well in his rifle. He switched to the Nosler Partitions and his rifle shot better.
I would think the TBBC would be a great bullet for what you intend to use it for. Take some ammo and targets to the range and let your rifle decide if it likes shooting the TBBC?
You still have time to special order other ammo for your 35-Whelen if you need too? IF the TBBC ammo does not shoot well in your rifle? The Nosler Accubond or Partition will expand not explode on impact at close range.
I can not think of a better black bear rifle than a 35-Whelen.

Have fun & good luck hunting,

W.K.