How can you get rid of bulging leg veins?

Depends on severity: If by bulging veins you mean varicosities you can help with support hose, elevating your legs when sitting and working on weight loss if overweight.

Next step: After the conservative measures, that dr. Hill mentioned, have been tried, if you aren't satisfied with the results, see a vein specialist (phlebologist). Treatment options for the bulging veins can be discussed. Nowadays there are a number of very successful treatments for varicose veins that safe, easily tolerated, performed in the office, and which have essentially no down time.

Close leaking valves: Varicose veins are a result of malfunctioning valves usually in the saphenous system. The first step in treatment would be to obtain a venous reflux ultrasound to make the diagnosis and help plan treatment which could be laser or radiofreqency closure of the valves usually with microphlebectomies and possible sclerotherapy or ultrasound directed sclerotherapy. You should see a vein specialist.