Two things you can do to make things easier on yourselves.
First - cover up. You know where the water flings. While avoiding it yourself, cover things in the line of fire. I have my set of cardboards which are form fit to the top of my tablesaw, whose top is 4 feet away from the lathe 9:00. After a bad experience caused, I believe, by not brushing my clothing off prior to going to the necessary, they also cover the jointer to the left of the saw table. I leave them where they are as I carry out the mess.
Which is the second point. No better place to direct the shavings than where you aren't, so adapt your turning style a bit to minimize travel distance, and put your collector there.
http://i35.photobucket.com/albums/d160/GoodOnesGone/Forged-Peel-Long-View.jpg I rough a couple three pieces and then do the Santa up the steps with the bag. Since my lathe is up against the wall, I can just allow the inside shavings to fall where they may. Simple thing to scoop them up and drop them into the bag.
http://i35.photobucket.com/albums/d160/GoodOnesGone/Forged-Peel-Inside.jpg Wet wood, even red oak, cuts in long shavings, so there's very little sweep-up. Don't make 'em "fly," let 'em fall.
If your lathe isn't up against the wall, make one. The benefits are visible here.
http://i35.photobucket.com/albums/d160/GoodOnesGone/ContactSheet-1-1.jpg Cardboard works, and if you fold it so it forms a cover for the stand behind as well as a wall, so much the better.
Remember to brush your clothing off before you walk through the rest of the shop, and/or leave the covers on until you're through with a rough session. Goes for any wood, especially the acid ones like oak and cherry.