For me, there are two different verbs here - one without "up" and one with it. If we say "Make the bed", it usually means "Put the sheets etc that are already on the bed into a neater position". With "up", I would expect the sheets etc to be somewhere else (such as in a cupboard or on a chair near the bed). If I were expecting an overnight guest at home, I might say to someone "Please go and make up the spare bed ready for Helen's arrival".
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