People say the verb inquire can be bitransitive (i.e., ditransitive) and also monotransitive. I can find many examples of its monotransitive use, but none about bitransitive.
Could you show me how it is used as a bitransitive verb?
Inquire is neither ditransitive nor monotransitive.^ A ditransitive verb is one like give (in some of its uses) that takes two objects:
I gave the dog a bone.
A monotransitive (or plain transitive) takes just one object, as gnaw does (in some of its uses):
The dog gnawed the bone.
Inquire can't be inserted into either of these syntactic frames in modern English (but see StoneyB’s answer and rogermue’s dated enquire the time):
*I inquired the time.
*I inquired the boy the time.
Instead, complements of inquire must be sentential for direct objects (the object of inquiry) or prepositional (the person to whom the inquiry is directed):
I inquired what the time was.
I inquired of the boy what the time was.
In a certain sense, inquire isn’t intransitive, then, either (as arrive is). Rather, its semantic argument is subject to a syntactic restriction: it can only be expressed by a sentential complement (what the time was), not by a noun phrase (the time). This contrasts with ask which is happy either with sentential or nominal complements:
I asked the time.
I asked what the time was.
I asked the boy the time.
I asked the boy what the time was.
The syntactic contrast between ask and inquire (and other pairs of verbs), which obtains despite their semantic similarity, was the subject of an important paper in theoretical linguistics by Jane Grimshaw.
^ I've never heard the term bitransitive in any grammatical work. So, I'll leave it aside in favour of ditransitive.
In Present-Day English, inquire is not used ditransitively (or bitransitively!) as, for instance, ask is. The person to whom you direct your inquiry is expressed with a preposition phrase:
I inquired of them whether the train was on time.
This was not always the case, however. According to OED 1, s.v. Enquire, that person might at least as late as 1682 be expressed in the same way as person of whom one asks:
[The Bible] was fram'd at first our Oracle t'enquire.
And OED (2.c.) even gives an instance, from 1400-1450, of actual ditransitivity ('with dative of person, or double object'):
a 1400-50 Alexander 1110 Enquire me noȝt þat question, for I queth þe it neuer.
There are two spellings: to enquire and to inquire, especially American English. to enquire can have a lot of preposition objects (about sth, after sb, of sb whether, into sth) and it can have two objects ( to enquire sth of/from sb) - He enquired the time from a passer-by. (elevated style)