I just pack it (well!!!) and put it on my board. Works well with TwinTip and Foil.
The key is, to pack it well. Not how were to put it
So you get a manageable, small enough package. Packing onto board works well, even when there is some water inside the kite. Which happens most of the time. That part will still be in the water and will slow you down. I never felt the need to tie it to my board with leash, but would be possible. I wear no Lycra and have no mesh bag - would both be helpful I guess. Just don't expect to be able to lift the package out of the water completely, there will be too much water inside 90% of the time... I pack/roll the kite in the water and drag it onto the board, impossible to lift it.
I sit on my board, hold it with legs.
I wrap the lines onto bar as much as possible, pulling the kite closer, so I can just reach one tip. Part of bridle will be on the bar after that. I move the kite in front of me to get to one tip. The other tip will get closer to me already, because of short bridles. I fix this tip and the bar on my lap. I pull the pother tip to me with bridle lines. Holding it up, so the middle part goes away from wind (if there is enough wind). Put tip on tip. Bar on top of both tips, Depower line /QR sticking out to the front, all bridle lines to the back (important for quick untangle at the beach). Tidy up the first part of kite from tips to center (so both halfes lie on top of each other cleanly), Roll in the bar into kite a few rounds, as far as it is possible - now I move the kite in front of me to get both halfs laying nicely on top of each other and open dump valves/zipper, After that back to the tips, roll a few more rounds while pressing air out, wait for air, roll again... while rolling I put bridles into the kite, if possible there should be a compact roll with no bridle lines hanging out and QR visible from front side. (Bridles/QR important for untangling later - if that didn't work it just takes longer to get the kite flying again later). I Roll/press as the part around the bar as good as possible to have minimum of water. With this method I have most water in the back part of kite... So pull the part with bar on and over the board, fold the bar-part onto the kite, pull a little more and fold again. Now the kite should be on the board but the back part with a lot of water inside will hang over the edge of board. You can press out some water, when folding, but it is not possible to get all water out IMO.
At this point you can use leash, mesh bag, lycra to fix the kite better... I sometimes pulled the bar out of package and wound the depower-line/QR around the package, but normally I can swim home as is.
Swimming is painfully slow, but I never had problems to keep the kite on board and hold it with one hand.