Am at Abdul Jaum and no quest is offered, haven't exchanged the weapon at all yet. Any requirements other that lvl 55? Char I am on is 57.

You must have a BA weapon in your inventory to actually get the BA exchange quest. However since you can now actually get BA weapons for every class if you followed the main quests. The reason the BA exchange quest is there is for characters who have already progressed pass the main quest where you actually acquire the weapon which is after beating Ferrid Boss in Omar Lava cave.

Hopefully this helps you out.

Try unequiping it if you have it equipped when you speak to the troll