I remember in nursing school trying to get every last microscopic bubble out of the tubing.
Here are my mostly serious suggestions:
It's impossible within the time frame allowed. :-) So, relax and just do your best. Be sure to roller clamp the tubing before spiking the bag. If you don't, you'll end up with a whole tube full of air and fluid. Squeeze the drip chamber half full and then *slowly* run fluid through the line. Fast fluid rates trap more air along the way. As the fluid moves along, invert each injection port and give it a good flick as the fluid moves past. Those ports are the worst offenders for trapping a little bubble of air and then letting them loose into the fluid later when you think you're done. Another really bad spot is the pump section of the tubing. For some reason, you get lots of bubbles on the wall of that section. Invert that whole section, holding it tightly between your hands and use one finger to pluck it like a guitar string. The plucking also works great on other sections when there are fine bubbles on the tubing wall. Just remember that if you're trying to remove bubbles high up in the tube, you have to move that air all the way down. It breeds more bubbles like rabbits. So, get them early.
If all else fails, whip out a 10cc syringe when the instructor isn't looking and aspirate the bubbles from each injection port.
And remember that this is an academic exercise. I've never actually seen a nurse stand there and get all the little bubbles out in practice. A few tiny bubbles won't hurt anyone and are really inevitable.