I recently replaced my master cylinder, line, and slave cylinder. I used no special tools or fixtures or the likes to bleed the system. I first 'bench' bled the MC while on the car. Hooked the new line to the MC. In back with the line hooked to the slave, I left the slave uninstalled with the push rod pointing towards the floor. This is easy since the clutch line here is a flex line. Positioned this wat the bleeder screw is at the top. My son would press once on the clutch and hold. I would pop the bleed screw and retighten. Rinse and repeat until fluid was pushed all the was back to the slave, filling it, and finally coming out the bleed screw. I kept an eye on the fluid level and had to top off several times. I was able to push the slave's rod in to make sure no air was in the cylinder. Once I was satisfied with the bleed I then actually bolted up the slave to the engine. This worked for me.
Yes, it sounds like your MC is bad. My slave doesn't have a heat shield. Could be previous owner removed it. I have no idea. Since you're thinking of replacing the MC and slave (I think it is a good idea), they'll be empty. Just blow out the line with air. Inspect your line thoroughly. Now is the time to replace it. Mine was corroded. The fitting at the slave was corroded to the line, not in the slave. When I turned it, it twisted the line breaking it. You're thinking of replacing two of the three parts. Go the whole nine yards and replace your line too. Doubtful you'll have to ever mess with your hydraulic clutch linkage again.
'88 Formula, red on gray
[This message has been edited by oneinch (edited 11-15-2020).]