Bulging vein on left cheekbone. Would a vascular surgeon be the right doctor to address this or am I stuck with it?

It is difficult to assess your blue cheek vein without a photo but it sounds as though this would respond to laser treatment. Fat transfer does not address veins so I would not have expected improvement of the vein following this procedure. I would recommend consultation with a board certified physician experienced in using the 1064nm laser for vascular treatments. Best wishes.

If it is indeed bulging as you describe, ultacision microphlebectomy would be a rather straightforward treatment. I combine it with sclerotherapy immediately before excision to minimize bruising. Expect to spend $1500 to $2000 for such treatments on the face. look for a vein specialist or a plastic surgeon who is comfortable dealing with vein problems on the face. 

There are several doctors who can treat this vein but a vein specialist or vascular surgeon would be appropriate.  Depending on the size of the vein and its location, there are several options for treatment including sclerotherapy, laser or microphlebectomy.