Is there a treatment to hide these blue veins throughout my face?

Not related to diet.You could take some bioflavonoids to keep your veins healthy. However, these can easily be treated in the legs with sclerotherapy and or cosmetic laser. The same can be done on the face using long pulse dye lasers. There is nothing you can do about the genetics of having a fair skin color and thin skin other than to not smoke and avoid exposure to the sun with high protection SPF.See the link below about bioflavonoids. Dr Karamanoukian

Blue facial veins are very common and usually can be treated with sclerotherapy or topical laser. They tend to be more prominent in fair skinned individuals and there is a hereditary component to them.  See  a vein specialist or someone with experience in treating these kinds of veins.

I have treated blue veins on the face (especially those around the eyes) very successfully with YAG laser.  This is a sophisticated laser procedure which requires special expertise and care.  This type of treatment would not be covered by insurance.  Veins on the legs are different than veins on the face.  Laser is not used as commonly for leg veins.