Just a bit of clarity required. If burning bridges has been played does that:

-stops LoW Catelyn from jumping into the challenge from you hand completely

-she enters but cant go back

-does something completely different

Thanks in advance

You can still use Catelyn because her ability is on a card that is out of play. It is in your hand, so doesn't count as being in play when you trigger the ability. When you trigger the ability it also sets up a lasting effect that says "At the end of the phase, return this card to hand" So it is set up at the initialization of the ability, and as such will still return catelyn to your hand at the end of the phase.

Excellent thank you very much for that incredibly quick response.

So is it fair to say that because it creates a lasting effect - fortified position would have no effect either in regards to how she plays.

Yes that is correct.