I'm not yet knowledgeable in the art of bow making but I am learning fast. One thing I do know from architecture and furniture making is that dowels do not resist shear well. Another words, when the bow bends, it isn't the bend that is causing them to pop off, it is the shear of the woods trying to slide by each other. For example, take a deck of playing cards and bend them. Notice that the edges stay paralleland you can now see a little bit of every card.
As others have mentioned, probably the best way to do this if you are going to allow bending in the handle is to make the handle out of multiple laminations. What this does is reduce the amount of shear on each glue joint. The ratio is simple:
1 handle lam = 100% shear between bow and handle
4 handle lam = 25% between bow and each lam.
If you have to use the dowels, the best way to do it was the way that Springbuck said, at an angle because this created more dowel surface area at the connection between the bow and handle. You can see what I mean if you cut a dowel in half perpendicularly, and then cut it in half at an angle. The angle cut has more of an oval shape, equaling a larger surface area.
Like I said, I'm no expert and I apolopgize for the physics lesson, but at least it is something to think about.
Rick