Summary if the problem, bridge is split into 2 steps.

• The bridge is calculated and connected.
• The edges from the bridge are then subdivided and made into a curve.

In the case where both loops are on a flat plane, its possible that the curve direction selected is different to the winding direction used when connecting the bridge.

For this to work as expected, either:

• the bridge normals used for calculating the initial bridge would need to be passed to the subdivision function.
• the winding of faces would need to be evaluated to calculate the normals for the curve.

Note that its possible to use an entirely different method of calculating handles, however this would need to be applied only for flat cases, which are tricky to detect since there would be some threshold which loops would not be considered flat, and this may give unpredictable behavior.

This whole situation is kind of a corner case, when bridging between 2 loops which are exactly aligned next to eachother, then applying curvature -it's not very obvious what the outcome should be regarding curvature. Using face normals one can be selected, so its possible of course. But still something the bridge tool isn't really setup to solve well.

Closing this report. If someone likes to solve its fine, but this is really at the limit of whats supported by this tool.