If you want to take blood samples from living bullfrogs in the field maybe the easiest way is to use cephalic vein, femoral vein or the ventral abdominal vein of the animal. But collect blood from fresh carcass you should take straight from the heart. You can find the attached paper dealing with the sampling of living animals through cephalic vein. This method could be use efficiently in male frogs with hypertrophied forelegs.
Heart is the best source especially when it still beats (right after decapitation). Use small seringe and just pop the heart wall. It depends how big sample you need but from living frog best way (in my opinion) is to puncture vein on inner side of thigh. gently puncture it with a needle used by diabetic to puncture their fingers (just needle. That penlike device would propably mess froggy bad). When you see drop of blood just apply glass capilary tube and let the physics work.
I've done that with smaller species but bullfrog is a frog afterall.
Isolation of blood by cardiac puncture is the most desirable method which is followed globally. Making use of an insulin syringe for the same can be recommended as the insulin syringe has a smaller aperture as compared to the other larger syringes. Protein (total) is usually estimated in the serum of blood. Hence, avoiding the anticoagulant is suggested.
The ventral abdominal vein is the most frecuent site to obtain a good blood sample. Using insuline syringe and fine needles, previously heparinized to avoid hemolysis.
All my suggesttions come from my experiences in blood collection of turtles, and I found the vascularity in turles and frogs are similiar. If you want to collect the arterial blood from living frog, I suggest you can process from the arteria femoralis; and if you need vein blood, maybe jugular vein could be helpfull.