The reason the dealer recommended his Bridgestones is because he wanted to sell you some - that's it. They wouldn't have been any better than the Dunlops. The business about there being 'a known problem with the Dunlops wearing quickly' is either ignorance or bulls**t on the part of the dealer.
The overwhelmingly likely reason for rapid and uneven tyre wear on the inside or outside edges, such as is being described in this forum, is incorrectly adjusted tracking, as one or two people seem to have realised. Simply get that adjusted (properly, by a reputable independent tyre dealer) and your problems will be solved. No need to go anywhere near a Honda dealer.
(It's perhaps worth mentioning that pre-facelift Jazzes do sometimes have a tendency to wear both edges on the front tyres. This is a feature of the design of the front suspension and there isn't much that can be done about it, other than swap the tyres front to back to try and maximise their life. I stress, this problem wears both corners of the tyre and does not cause the characteristic feathering on the edges of the tread blocks that points to poor tracking. If you have wear just on the inside edges or just on the outside edges, perhaps with feathering of the tread pattern, then you have badly adjusted tracking.)
As for what tyres to choose, get the cheapest you can find from somewhere like Black Circles. They'll be fine. We're talking family hatchback being driven moderately and sensibly (hopefully), not F1 racer.
