Yes, it should be possible to perform a grafting procedure to restore height to the upper part of your bridge. This area is called the radix and radix grafting is a fairly common procedure. It's not especially risky to perform. The main issue is that tissue is needed to graft to the area. This often includes either cartilage (septum or ear for example) and/or fascia.
If that's all that need to be done then a closed rhinoplasty approach may be used to perform the surgery, avoiding external incisions.
You can read more about bridge augmentation at my web reference link below.
Revision rhinoplasty is always harder than a primary rhinoplasty due to scar tissue and less predictability of healing. Nasal cartilage can be harvested from inside the nose to build up the bridge, if it has not been removed with a previous septoplasty. In cartilage depleted noses, we use ear cartilage. A Silastic nasal dorsal implant can also be used when the nose and ear cartilage have been depleted. For many examples of building up a shallow bridge line and our price list, please see the links below
For smaller changes, fillers can often be a good option. For larger changes, either bone, catilage or synthetic dorsal only implants are all options. I will often utilize synthetic onlay for straightforward deficits. While there is a slightly higher risk of infection, it is still small and the cost, predictability and ease make it a fair trade for most patients in my opinion.
My fee for something like what I dexcribed would be $2500-$3000US. It is an outpatient procedure, under one hour with minimal recovery. I hope this helps.