
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?

to ask
To politely ask or invite someone to do something or to come somewhere.
Der Gastgeber bat die Gäste zu Tisch.
The host asked the guests to come to the table.

to need persuading
To hesitate and comply with a request only after repeated prompting; to be coy or reluctant.
Nimm dir doch noch ein Stück Kuchen, lass dich nicht so bitten!
Go on, take another piece of cake; don't make us ask you twice!
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 is appropriate when you want to know whether you have permission to do something. Bitten, on the other hand, directly expresses the request for that permission and is often used with „um“. Both are possible in the same situation, but the sentence structure is different.

Ich bitte meinen Chef um Erlaubnis, heute früher zu gehen.
I ask my boss for permission to leave early today.
Ich frage meinen Chef, ob ich heute früher gehen darf.
I ask my boss if I can leave early today.