Is there a difference between the verbs "bieten" and "anbieten" in sense "to offer"?
There are some typical uses where one fits much more than the other: For example one would say:
Diese (Arbeits-)Stelle bietet ihnen die Möglichkeit, sich persönlich weiterzuentwickeln (This job offers you the opportunity for personal development)
IMO nobody would say "anbieten" in this context. Another case would be such context like offering a seat or refreshments:
Darf ich ihnen eine Tasse Kaffee anbieten? (Would you like a cup of coffee?/May I offer you a cup of coffee?)
Here only "anbieten" fits (I don't know the exact reason, just that I would register "bieten" as odd).
As other answers already stated, there are areas where both are fine.
Ich biete Hilfe an.
That means offer help, with using
anbieten. Theoretically, you could say the following, too:
Ich biete Hilfe.
But you can say the following:
Ich biete 30€ bei der Auktion.
Here you can't use
anbieten, because here, the meaning isn't offer.
In general, you can use
bieten every time you can use
anbieten, but not the other way round.