I use a similar setup to the turkey baster method now, it’s a vacuum pump bleeder with the hoses reversed so it blows into the catch can that’s filled with brake fluid. It works great, no pumping, it pushes the fluid backwards through the system.
The other way I used to do it was crack the bleeder at the caliper, fill the reservoir and let it gravity bleed until fluid is seeping out the caliper then close the bleeder. Now slowly pump the brake lever, you’ll notice a couple bubbles after every pump come floating up in the reservoir. Keep pumping every 5~6 seconds until the bubbles stop and your done. It does take about 15 minutes of pumping tho.