Originally Posted by
oris
Amazon is your friend here.
I would recommend getting a Shimano bleed kit including the little adaptor for the funnel; this is a separate piece to use the funnel on road shifters. An olive/barb tool is handy to install the barbs but you can get away with a vice and hammer if you're careful. I included a link to the one I use; it has a side cutter for hoses as well. Otherwise make sure you have a 7mm wrench for the bleed ports on the calipers since it's not usually included in metric wrench sets.
Just use the red wedge that the shop gave you to bleed the brakes.
Shimano Funnel Adaptor
https://www.amazon.com/gp/product/B0...?ie=UTF8&psc=1
Olive and barb tool
https://www.amazon.com/gp/product/B0...?ie=UTF8&psc=1
It's orange and it's supposed to go between the pads, definitely DO NOT use it. You want the yellow bleed block specific to your caliper. You NEVER want to bleed brakes w/ the pads in the caliper. The new Shimano bleed kits are available in road and mountain so you don't need the adapter.
ETA: Shimano's List of tools:
List of tools to be used
The following tools are needed for installation/removal, adjustment, and maintenance purposes.
Tool
2 mm hexagon wrench
2.5 mm hexagon wrench
3 mm hexagon wrench
4 mm hexagon wrench
5 mm hexagon wrench
8 mm hexagon wrench
8 mm spanner
7 mm box wrench
Adjustable wrench
Slotted screwdriver
Cross head screwdriver [#1]
Slotted screwdriver (nominal size 0.8 × 4)
TL-BH62
TL-BR001 (syringe and tube)
TL-BR002 (oil funnel and oil stopper)
TL-CT12
TL-BT03S
TL-LR15 / TL-LR10
Micrometer
Hexalobular [#8]