Put a pan of lightly salted water on to boil. Boil the asparagus, if fresh, briefly, for 30 seconds or so, then drain well and set aside. (Asparagus in jars does not need cooking.)
Remove the larger stalks from the watercress and chop it. Place the mayonnaise and mustard, if using, in a bowl and stir in the watercress.
Split the bagels in half and toast under a preheated grill. Spread the halves with the flavoured mayonnaise. Top with the beef and asparagus spears and wrap securely. The bagels can be refrigerated for 1–2 days.