you can only use 57g of wholemeal bread as a HEb, I can pretty much guess that a bagel is much more than 57g, also they are made much differently to bread, as are wraps. Most have oil in them and many more ingredients you wont find in wholemeal bread, hence why they cant be used as a healthy extra.
Also I know slimming world is not about counting calories, but for instance 2 slices of wholemeal bread weighing 57g in total (so qualifying as a HEb) is usually under 120 calories (so 6 syns max). 1 New York Wholemeal bagel is 223 calories and they weigh 90g approx (so 11 syns).
The only Healthy Extras you can use are the ones listed on the Slimming World list (which is updated frequently as Slimming World find new products), there is no substituting for others unless it is in the scenario as ermintrude pointed out and again it must be wholemeal.
Any bakery item which doesnt qualify as a healthy extra can always be worked out using 1 syn for every 20 calories, as they have no free food allowance.