I think that air in the system would make the clutch spongy, not stiff.
Bleeding is easy. Get a piece of plastic hose that fits over the bleed nipple on the clutch slave (you will need to remove the little rubber cap of the bleed nipple).
Put the hose over the bleed nipple and put the other end in a small container.
Give the clutch lever a couple of good pulls and keep it pulled in.
With a wrench gently loosen the bleed nipple and watch the fluid that will come out, look for bubbles.
Tighten the bleed nipple before you let go of the clutch lever, to prevent air from being sucked back in.
You can repeat this a couple of times, but make sure you don't empty the clutch reservoir (and get air in the system).