[wiswind]

You might try to see how it works to just slip the tube over the bleeder without any adaptor.
I have used a SMALL tapered nipple and pressed it up inside the hole in the bleeder.
I see a couple of those adaptors in the picture you posted, bottom of the picture, just to the right of the 2 short clear hoses.

What I have found to be the major cause of problem when bleeding brakes is that air leaks through / around the threads of the bleeder screw.
What I have done to correct this is to REMOVE the bleeder screw and put Teflon tape on the threads....and re-install the bleeder.
You can get teflon tape in the plumbing department at your hardware / home supply store.

The last time I bled my brakes.......I bought a cheap "1 man bleeder" at AutoZone.
Just hook it up.....and open the bleeder screw slightly......and pump the brake pedal a couple times.
However, the same applies.....gotta have a good seal with the hose/adaptor and threads of the bleeder screw.
I did that because I could not find my pumper unit......of course, I found it the next day when I was not looking for it........

Looks like you could do that with your unit.....connect the line to the bleeder hose using one of the small tapered adaptors......run the tubing to the bottle....and mount the bottle at a location that is slightly higher than the bleeder screw / caliper.
When you press the pedal......fluid will go into the line...and into the bottle....but you will have fluid in the line.....so when you release the brake pedal......you will draw some, but not much of the fluid back into the caliper (but not air), then press the pedal back down again.
You press the pedal down and release SLOWLY.
Most of the fluid that goes into the caliper when you release the pedal comes from the master cylinder, not the fluid that you pushed out through the bleeder.

As you know, don't forget to top off the master cyinder.......don't want to pump it dry.