Have you checked for fluid leaks at the backs of the master and slave cylinders? If you get air from the slave right away, I'd say that's the problem. Get the slave rebuild kit for the Toyota MR2 as described in TopNotch's article in the Tech section.
Pumping the clutch to bleed it can blend and scatter the air bubbles into the fluid. I use a variation of the gravity bleed method. Lifting the left front of the car to a point the wheel is about 4-6" off the ground, open and top off the master cylinder. Leave the top off the brake fluid and the master cylinder. Go to the rear and open the slave bleeder. You can tap on the slave lightly to dislodge any air that may be stuck at the pushrod end. Watch the master cylinder and refill about 3 times, each time before the fluid reaches the bottom. After the 3rd refill, as the fluid reaches the FULL mark on the reservoir, go to the rear and close the bleeder valve.
If you rebuild the slave, you can cap the fluid line with a vacuum cap found on the HELP rack. Then when reattaching the rebuilt slave, you can use the gravity bleed method by just holding the slave in a vertical position to bleed the air before installation.
This is a one-man method and requires only a jack and a wrench. You can eliminate the jack if you have an incline where you can park the left front wheel straight uphill of the right rear, at a 45 degree angle.
Sometimes it takes a while to get the MR2 rebuild kit. I waited on Advance for about 3 weeks before they told me the one they had in Virginia had been sold. I have one I can loan. You can order one and when it comes in, repay me. That way you'll get the Sport on the road quicker.