Bunions are an enlargement of the medial side of the joint at the base of the big toe that can become painful. Bunions are caused by a combination of hereditary factors and poor fitting footwear. The only effective way to get rid of bunions is with surgery. This means that treatment is aimed at reducing pressure on the big toe and the joint by using better fitting footwear and pressure relieving pads.
If you want a pair of running shoes that will accommodate a painful bunion, then they have to be wide enough for what could be called the anatomical shape of the foot.
There are not a lot of running shoes that achieve that criteria. The only common brand is the Altra running shoes and they are the ones that are most commonly recommended for those with bunions. They are much wider in the forefoot compared to other brands and can accommodate an enlarged big toe joint.