bitten um
to ask for
To express a polite request or wish in order to receive something or have something done.
Darf ich Sie um einen Moment Geduld bitten?
May I ask you for a moment of patience?

to ask / request
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to ask for
To express a polite request or wish in order to receive something or have something done.
Darf ich Sie um einen Moment Geduld bitten?
May I ask you for a moment of patience?

When asking for something, the structure is always: jemanden (accusative) um etwas (accusative) bitten (to ask someone for something). The preposition 'um' (for) is fixed with the verb here.
Ich möchte dich um einen Gefallen bitten.
I would like to ask you for a favor.
When asking someone to do something, you use the structure: jemanden (accusative) bitten, etwas zu tun (to ask someone to do something). The verb is followed by an infinitive construction with 'zu' (to).
Ich bitte dich, leise zu sein.
I ask you to be quiet.
You can recognize the meaning from the sentence structure. If 'um + accusative' follows, someone wants to have something (m01). If an infinitive construction with 'zu' follows, someone is supposed to do something (m02).
Kann ich dich um einen Stift bitten?
Can I ask you for a pen?
The expression 'sich bitten lassen' means 'to hesitate' or 'to need persuading'. It is almost always used in the negative prompt 'Lass dich nicht bitten!' (Don't make us ask you twice!), to encourage someone to accept an offer.
Komm, iss noch ein Stück Kuchen, lass dich doch nicht so bitten!
Come on, have another piece of cake; don't make us ask you twice!
to ask
'fragen' and 'bitten' can both appear in polite conversations. 'fragen' is used when you want to get information or ask for permission. 'bitten' is used when you want someone to do something or give you something. The difference is important: with 'fragen', you mainly expect an answer. With 'bitten', you expect an action or help. Learners confuse the words because in both cases you want something from another person.

Am Abend bitte ich meine Schwester um Hilfe beim Aufräumen.
In the evening, I ask my sister for help tidying up.
Tim fragt die Lehrerin, wann der Test beginnt.
Tim asks the teacher when the test starts.