I wouldn't do it that way. I used liquid CYA in a bucket like that, and got it into the pool OK. But then went to get that last bit out of the bottle, by adding water and swishing it around, and then poured that into the pool. What I thought was a little bit, was a big chunk of residue, probably similar to the dry stuff, and it settle on the bottom and before I could brush it off, like less than a minute, it burned my brand new pebble. The stain is still there. I'd be concerned, doing it your way, that some amount would settle in the bucket and then just dump out, or that what I thought was dissolved in the bucket wasn't, and that it would settle on the floor. Admittedly, I'm paranoid about the stuff now, so am being extra cautious. But I was cavalier before, and thought I could come up with a good enough way, all on my own, and now I'm sorry. What's your rush?
So that taught be a few things.
1.
Follow TFP instructions! To the letter, if you can. These guys have been-there-done-that, and are very careful about delivering to the members here the very best way to do something. They might sound casual or brief the way they describe a process, probably because they have to do write it out over and over and over, but there's a reason they do things the way they do, and I've found it's best for us newbies to just defer to their wisdom. They're generous with their instructions, but they don't always expound on how those instructions were developed, or the mistakes that were made along the way.
2.
Adding CYA is not like adding chlorine, or calcium. It's pretty strong stuff and has the potential to damage/stain a pool finish, very easily, and very quickly, and there's no fix.
3.
Even if you could add it faster and easier, it takes a day or two for it to register on a CYA test, so you're not saving yourself much time by rushing it in.
Now, that all said, I don't like the "hang it in front of the return" process, because of the potential for the pump to stop or the sock to leak and having the CYA pile up on the floor before you notice (Paranoid! But, my pump did stop while I was adding, so that's a real-world possibility). So I use one of their alternate "mostly sanctioned" methods, by putting the sock in the skimmer. It gets good flow there, and should something go wrong, it will most likely go wrong in the skimmer, and not on the pool's finish. The down side is that the CYA can then gather in the filter and be subject to backwashing (which isn't an issue for me and my cartridge filter) and/or taking a little longer to works its way into the pool water. But for me, that's worth the extra time to be extra careful. I use a "delicates" laundry bag instead of a sock, which sped things up a bit (my socks were too thick, and I don't wear panty hose!).