1997 Infiniti Q45 Powersteering pump high pressure hose

Air in your system won't cause it to back up like that. This sounds like you simply had too much fluid in the resevior. When the system heats up, the fluid expands. So if there's too much fluid in there when it's cold, it'll overflow when it's hot.

Also, if you have dirt in the system/pump, or there's a blockange somewhere, this will cause the fluid to back up. So when you had your hose replaced, it's possible they contaminated the system.

If you still want to bleed the system, here's the procedure:

Raise front end of vehicle until wheels clear ground.
Add fluid into oil tank to specified level. Meanwhile, quickly turn steering wheel fully to right and left and lightly touch steering stoppers. (If there's air in the system, your fluid level will decrease as the air escapes)

NOTE: Repeat steering wheel operation until fluid level no longer decreases.

Start engine.
Repeat step 2 above.
Incomplete air bleeding will cause the following to occur. (When this happens, bleed air again)

1.Generation of air bubbles in reservoir tank
2.Generation of clicking noise in oil pump
3.Excessive buzzing in oil pump.

Fluid noise may occur in the valve or oil pump. This is common when the vehicle is stationary or while turning the steering wheel slowly. This does not affect performance or durability of the system.