Bullseye is an excellent powder for target loads, and for standard velocity loads in cases like the 32 S&W Long, and 38 Special, and 45ACP. I have fired cases of reloads with Bullseye in 38 Special.
However, even when it comes to big cases like the 44 Spl, 44 Mag, and 45 LC, Bullseye will give you excellent accuracy, but it won't give you top velocity. And I don't recommend a magnum primer with it.
I would recommend, in the 44 Mag, Alliant 2400. I have used that powder for decades, with a 240 L. I have used charges between 17.5 grains, will give just under 1200 fps, to 22.0 grains, which will give under 1400 fps in my pistols. The heavier load is Elmer Keith's classic load in the 44 Mag. It is still one of the best full power loads in a 44 Mag.
I have tried powders such as Unique, AA#9, Blue Dot, and H110. H110 will give the highest velocities, but is not flexible because you can't safely reduce charges. I loaded up 500 rounds with 8.5 grains Unique, that was just at 1000 fps and it was fantastically accurate. But for me, I have found 2400 to be the most satisfactory and most flexible of the powders I have tried in the 44 Mag.