Both mean the same thing with 'Jump out of' being the more frequently used one. There is a slight difference in the tone however. "jump out of" stresses on the destination with the act of jumping out stressed more. "Jump out from" lays a little more stress on the source of the jump, i.e. the sheet. Also in this case, Jump out from his sheet sounds a little wrong. Jump out from his bed makes more practical sense :D

"When the clock rang, James jumped out "of" his seat* immediately" is correct. A "sheet" is the cloth put over the mattress of a bed; "sheet" is not correct in this sentence. But "when the clock rang, James jumped out of his bed* immediately" is correct.