Is there a concise, non-colloquial alternative to the phrase
"make/made/making the bed"?

Straightening/Arranging the bedclothes?

- Hammer

feathering the nest?

The 36th definition of "make" as a verb in the Oxford English
Dictionary is "to prepare (a bed) for sleeping in." The usage examples
given with the definition go back to the year 1290.

Rather surprisingly, there doesn't seem to be an alternative phrase,
whether colloquial or not (except perhaps for the OED's pedantic
"preparing the bed for sleeping in"). I don't think hammer's
suggestion of "straightening/arranging the bedclothes" fits the bill -
indeed, that is something lazy people do instead of "making the bed".

It isn't colloquial.  This sense of "make" is within the standard
dictionary definitions of the word.  It's idiomatic:  that's just the
way we say it.  Why do you need an alternative?  "Make" (one word of
four letters) is about as concise as you are going to get.

So even though I'm not a researcher, I would say that the answer to
your yes/no question is no.

Archae0pteryx

When she made the bed, my grandmother used to say she was "changing the linens."

archae0pteryx-ga: You are correct, the phrase is idiomatic.  To answer
your question, I simply prefer to avoid idioms and colloquialisms when
I can.  How would I express the meaning of the phrase in formal
writing?

markj-ga: I suppose you are correct; however, "make" strikes me as an
"overloaded" word with too many definitions.

hammer-ga: I didn't realize it, but all my life I've used the phrase
"make the bed" to mean two distinct things: "replace the bedsheets"
and "straighten the bedsheets", the latter having to be done each
morning except when the former is done instead.  However, both of
these wordings seem unnecessarily awkward.  Now that I think about it,
it's probably impossible to reduce the syllable count of either to
less than five...

I'm curious what the literal translation of foreign equivalents of the
phrase would be.  Surely they don't all use variations of "make"?

Ah, nice question, gw:  what is the literal translation in other
languages?  I often use foreign-language dictionaries as well as half
a dozen or more English ones to help me gain an insight into the
dimensions and subtleties of a word or expression.  I'm sure some of
our bilingual and multilingual researchers and commenters could help
with that, but I do think it's a separate question, not implied in the
one you posted.

You can't avoid idioms.  They're all over our language (any language)
and may be as much a part of formal writing as they are of casual
speech.

Tell me, does the expression "change the bed" seem informal to you? 
That's the expression I find most familiar for the act of putting
fresh sheets on the bed, as opposed to making (or making up) the bed,
restoring the sheets to an orderly arrangement.  If it doesn't seem
too informal, well, that is the partner expression to "making the
bed," and I would argue that they are at the same level of formality
or informality, so if one would do, the other would too.

It seems to me that your real complaint is that the word "make" has
too many meanings.  That doesn't make it imprecise or informal, just
versatile.  Words such as "run" and "get," which have very numerous
meanings, are no less precise in any one sense just because they are
used in other senses, are they, do you think?

But if what you are really after here is a way to refer to the act of
making the bed in language that is at home in formal writing, you can
probably find fancier ways to say it, such as such as "smoothing the
bedclothes," or substitute expressions that make it sound more
impersonal, less like an act performed by a human being and more like
something that happens of its own accord.  In fact, what we're talking
about when we say "making the bed" is *not* preparing a bed for
sleeping in, because when it's made up, you can't sleep in it like
that.  You're making it look as if it had never been slept in and were
never going to be slept in, and maybe weren't even really a bed.  When
you're ready to sleep in it, you have to UNmake it a little.  I think
you want an expression that sounds as little like "making the bed" as
a made bed looks like something ready to be slept in.  And with that I
can't help you, apart from remarking that in writing that is too
formal for an expression like "make the bed," the act itself should
probably not be mentioned at all.  It will be done behind the scenes,
by the maid, who will make it look as if it were untouched by human
hands.

Archae0pteryx

I believe French, Spanish and German also use the equivalent of "make"
(respectively, "faire," "hacer," and "machen") in their expressions
for bedmaking.

In Shakespeare's time, there was a phrase "to make the door," meaning
to shut and lock it, or "make it fast."

"Why at this time the doors are made against you." (The Comedy of Errors, iii. 1.)

"Make the door upon a woman's wit, and it will out at the casement."
(As You Like It, iv. 1.)

The phrase, making, or, make the bed, was certainly in common use in
England as early as 1681. These are excerpts from the Old Bailey
criminal trial records.

1681
so that as she was making the bed she found it
1685
came upon her as she was making the Bed
1738
I was above Stairs making the Bed 
1740
to help her in making the Bed
1751
she was making the bed
1768
was making the bed 
1793
where she had been making the bed 
1795
parlour making my mother's bed

One for ?change the bed?
1771
the wife had a pair of sheets to change the bed 

I could not find any other phrase.

http://www.oldbaileyonline.org/search/keyword/

answerfinder-ga