What do you think of a 6 unit bridge from 10-15 with abutments at 10, 11, and 15?

It can be done, what you are describing is what is called "a long span bridge."  But the bridge will not likely have a long term prognosis.  Also, the lateral incisor, #10, is the smallest and weakest of all the upper teeth, and not the best tooth to anchor as an abutment (tooth supporting a bridge).  Since your are missing three teeth in the gap, and #14 will replace the larges of all the upper teeth with the strongest root structure, you should also consider implant treatment.  This way you would not have to drill #10 and #11 for the bridge.  Have an implant bridge with two implants, one in the area of #12 and the other implant area #14.  However, because the maxillary sinus is in that bone area, you might need to have an additional procedure called a sinus lift and/or bone graft, to have enough bone to place the two implants.  Either can be done (implant bridge or long span bridge), but clearly I feel that the implant approach would be the best and longest lasting, albeit more costly dentistry.

Can it be done? Yes. Is it a good idea? No. Due to a long span and "around the corner" design the useable life of this bridge will be much shorter than expected and may lead to eventually loosing abutment teeth.  As long as you understand the limitations of this design and your are OK with it, go ahead and do it, but you should consider other options, such as implants, or removable partial denture.