You'd have to do it in a Big mouth Nalgene 32 ounces 1 at a time and pour it into your bladder. Thats the way I do it. I wouldn't want to risk missing anything by doing it directly in the bladder. I could be wrong though. Sure other users will chime in.
I'm using a big mouth Nalgene and a 2L camelbak antidote. Sterilize the water in the bottle and transfer to the bladder. I like having the Nalgene for when I want to take some big gulps.
I also add a Human gear Nalgene Lid to my 32 ounce. Aaron showed this in one of his Gritty Bowman episodes and it works great. It keeps you from cross contaminating your water when you dip it or let the river lake water run into your bottle.
The human gear cap-cap is definitely worth it and only a very tiny amount of weight over the standard Nalgene lid.
If you're trying to cut weight using a bladder but wanting to use a steripen - you can take an old 1L platypus roll up bottle and chop the top off leaving a wide open "sleeve" that will weigh nothing. It works well to "scoop" water into it and then use your steripen to stir the water before dumping it into your bladder.
If you don't use a Nalgene for anything else - that may be the lightest, and most convenient method for treating water to fill your bladder.