If I leave it on ice I will pack the meat in ice open the drain plug and elevate the opposite end of the drain, put a brick under it etc. it will keep the water draining away from the meat.
This.
Usually do this for a full week.
Had a guy give us some backstrap two weeks ago. Once it thawed, I knew it hadn't been bled out as long as I do. Was a little more gamey smelling, and tasting, but we wore it out anyway!