3 ideas.
1) Tie your running Bowline around the climbing line like you did before. Then, put a biner in that loop as well. Tie your blackline to the biner. Then when you pull on your blackline, you're pulling on the biner.
2) Tie your running Bowline around the climbing line like you did before. Then tie a midline knot (butterfly, etc) next to the Bowline. Then attach a biner to the midline knot as in 1) above. This might improve the line of pull for the blackline. But, it might make it worse.
3) If you feel comfortable changing your system, use a delta (or pear) _link_ instead of the running Bowline, then tying the blackline to the _link_. The _meta_l should slide better on the rope where the rope is choked off against the branch. But, it involves changing your climbing system.

For new climbers: don't use a locking biner for this connection - you might end up hanging on the gate of the biner!