Using a Throwbag
'If a throwbag falls and no-one catches it, who do you hear scream?' (ancient mid-Wales proverb.)
Maybe its you
If you miss what is the back-up plan? Perhaps you are the back-up plan!
Where will they go?
When the swimmer has the line is there somewhere to rescue them to?
An eddy, some slack water? - If not move somewhere else.
Get the rope out
If there is time prepare yourself. Look at the river, where will the swimmer pass you?
Estimate the maximum distance you will have to throw, add 3-5meters, then take out any excess rope from your bag. Why do this? - Your bag will be lighter and easier to throw and there will be little excess rope in the water to get caught or tangle around the swimmer.
You may end up with spare rope on the bank (or neatly lap coiled in your hand, either way it should be prepared so it will run out without tangles which you can use to pay out if necessary during the rescue.
Is the swimmer aware of you? Shout to them.
If they can't see the bag coming it's unlikely that they'll see it when it's in the water. Encourage the swimmer to swim towards you to reduce the distance you have to throw.
Once the swimmer has the line it's your job to get them to the side. (obviously!)
Be prepared to be dynamic - move, allow rope to pay out, take in when appropriate.
The load you feel on the rope is also felt by the swimmer. The greater this pressure the more likely the swimmer will let go - or that you will fall over/in and let go. So move down the bank with the swimmer pulling them in across the current as you go.
Remember the rope
If you can't move down the bank then you will feel the pressure grow as you try to hold the swimmer against the force of the current... don't forget that spare rope you created by preparing yourself.
So as the pressure rises towards a level where holding (for you and the victim) is becoming tough, allow a little rope to slide through your hands to dissipate the force.
Use a drop bag
Better still use a 'drop bag'. Rescuer one gets as close as possible and passes/throws the bag to the victim, and then lets go. Rescuer two who has the remainder of the rope, should be positioned in the optimum position to actually retrieve the swimmer into an eddy with the least force possible on either themselves or the victim.