Casting while standing in water

I am new to flyfishing and after taking a lesson and practising for
hours at the park I thought I had a reasonable handle on casting, at
least to the point that I wasn't wrapping the line around my neck and
embedding a hook in the back of my head.

My instructor showed me how to haul on the front and back false casts
to build up line speed and then "shoot" the line on the final foward
cast. This works a treat at the park because the line gathered around
my feet snakes off down the rod until it bumps the reel softly at which
point I lay the line down and presto.

But alas, there are no trout in the grass. When I try the same
technique while standing in the river, the excess line is swept
downstream behind me in a large loop. There is a lot of weight on the
line from the water pressure and I have to really pull on the line to
recover any of it when I'm hauling and releasing on the false casts. I
can forget about shooting because there is no way I can build up enough
line speed to counter the water pressure on the excess line.

Should I fish from the bank so the line stays dry, or is there a
technique for this? I'm using a floating line.

Cheers.