For Shimano brakes, you don't need a syringe. Just attach one of these fancy guys to your brake on top, fill with fluid, and pump your brakes while draining out the other end. Way easier than using a syringe.
nope, you just open the reservoir connected to your lever, screw in the bleed funnel, add brake fluid to the funnel, then pull the brake lever and watch bubbles (if there are any) come up through the funnel. this gets any bubbles out of the upper part of the lines, which is where they would be introduced when cutting lines
http://www.amazon.com/Shimano-SM-DISC-BP-Funnel-Tool-Stopper/dp/B005G0BG70
As others said, the Shimano SM-DISC-BP funnel will thread directly into Shimano MTB brakes and will for the most part allow complete air bleeding.
It won't allow you to refresh fluid without a syringe and hose, which is pushed from the caliper bleed nipple up thru the system to the funnel in the levers.
For road levers you need the Shimano Y0C698050 funnel adapter
I don't remember what hose I bought at my local hardware store. To connect the syringe to the rear caliper.
In the end I ended up buying a Jagwire Pro bleed kit for both Mineral oil and DOT kits. Bleeding some friends' SRAM brakes with dual syringes has made me appreciate the simplicity of Shimanos system