Bulging veins behind my knee. What is the cause?

Generally  it is related to reflux of the GSV with tributary or excessery vein component. You need a proper evaluation with ultrasound . 

Hi Shelly Cameron, 
Varicose veins are very commonly located in the calves, behind the knees and thighs. The cause is usually an underlying vein valve leak (venous insufficiency). An ultrasound is highly recommended prior to treatment as in a small segment, varicose veins may represent an underlying clot in the deep vein system which needs to be addressed immediately. 
In a nutshell, an ultrasound of both legs including the deep system followed by a treatment plan. If you do not have any symptoms of venous insufficiency, a cosmetic route for treatment is your option. Non-surgical methods include ultrasound guided sclerotherapy.