The Master cylinder seems to bubble when pedal is depressed.

The most common mistake when doing repairs to the hydraulic system or when surprised by a sudden leak, is pushing the brake pedal to the floor. Crud and corrosion build up in the lower halves of the bores where the pistons don't normally travel. Pushing the brake pedal over halfway down runs the pistons over that crud and can rip the rubber lip seals. The symptom will be a low or a slowly-sinking brake pedal, and that often doesn't show up for two or three days.

To prevent this from happening, never push the brake pedal more than halfway to the floor unless the master cylinder is less than about a year old. Some people resort to pedal-bleeding with a helper too, and it's important to tell them to not push the pedal too far. I only use gravity-bleeding to prevent this problem.

As for which is the right master cylinder, there's at least two different bore sizes, and you can have a vacuum-operated power booster or a hydro-boost system that runs on power steering fluid pressure. Take the old master cylinder to an auto parts store and they will measure the bore to get you the right replacement if that's what is needed.

Since this is fairly common, my suspicion is, yes, you need a master cylinder, but if you have a way to do this, I'd feel better rather than throwing unneeded parts at the problem. If you can remove the lines from it and plug the ports, that should leave you with a real high and hard brake pedal. If it goes down right away or sinks slowly, it's leaking internally and must be replaced.

For this test it's okay if the plugs leak a little, but you don't want to run in anything that will damage the flare or the threads. An old line might have the same thread on the fitting. Just bend the line over to crimp it.

The bubbling you described could be air working it's way out. You should see a little spurt of brake fluid just as a helper starts to press the brake pedal, but that's hard to see with some reservoir designs. Once the pedal has been pressed halfway to the floor, you might see a spurt of fluid in the reservoir when the pedal is released. That is due to the rear shoes retracting, and suggests the shoes might not be adjusted up fully.

Before you get too involved, you might want to let each wheel gravity-bleed until clear brake fluid comes out. If at any time up to now the reservoir ran empty, there will likely still be air in the lines near the master cylinder even though no air comes out at the wheels. To get that air out, close all the bleeder screws, push the brake pedal slowly halfway down. It should take about 15 seconds to do that. Hold it there for a few seconds to give the air bubbles a chance to float back up. Now release the pedal quickly. As the fluid rushes back into the reservoir, any air in the lines will wash up there with. If a helper is working the pedal, you might see the air bubbles. Keep doing that as long as air is still coming out.

Once the air is removed, when you do the other steel lines, you can avoid having the reservoir run empty by placing a stick from the seat cushion to the brake pedal to hold the pedal down about an inch. That's enough for the lip seals to move past the ports and block fluid from running out.