This syringe and tube on Amazon is well made, seals well (no leakage I could determine), can pump or suck (we won't go there), comes with spare seals, and is not expensive. Should work just fine with 5606 fluid (the petroleum based red brake fluid as used in Schleichers:

https://www.amazon.com/gp/product/B0...?ie=UTF8&psc=1

Two things when bleeding brakes, if the caliper brake line doesn't enter from the very top, then an air bubble can be trapped within. Best to take off the caliper and clamp the piston in with a C-clamp (so it doesn't pop out and make a mess!), then with the caliper brake line at the top, pressure bleed from the bottom.

Be sure to empty the reservoir while doing this. On some brake systems you will need to bleed with, um, gusto, to move air trapped in the lines at any high points out and up. I have a small pump up garden sprayer for this that work nicely (the the syringe above should do okay for small jobs - a plus is it will also drain the fluid from the reservoir).

5606 can turn to goo, partially solidify after many years of not bleeding or changing fluid. This can be recognized as very low or almost no fluid pumping in from the bleed valve. On one system I removed the bleed valve and installed a temporary nipple - then really got so flow going to clear things out. To that end, you can also install a nipple in the lid of your brake reservoir, this will allow surplus fluid to be drained off during the bleeding process without having to repeatedly stop to drain the reservoir. (Hint, do not try to fashion a temporary drain system using a male catheter - this will create much sorrow and mess to clean up as the material is completely incompatible with the rubber which will fail in short order. I think if there's a dumb trick - I've tried it.)

Oh, it's also a good idea to exercise the cockpit brake lever a couple of times whilst bleeding.

Fun.

Enjoy,

bumper