The correct answer is: for.
The word “bargain” can be used in a number of ways, but in this context it means to expect or anticipate something. In the sentence “We did not exactly bargain for him turning up like that out of the blue,” the speaker is saying that they did not expect him to arrive unexpectedly.
The other options are not as likely in this context. The word “about” can be used to talk about something that is being discussed or considered, but it does not make sense to say that the speaker did not expect to discuss or consider him turning up. The word “for” is the most likely option because it is used to talk about something that is desired or hoped for. The word “of” can be used to talk about something that is a possibility or a risk, but it does not make sense to say that the speaker did not expect him turning up to be a possibility or a risk. The word “to” can be used to talk about something that is intended or planned, but it does not make sense to say that the speaker did not expect him turning up to be intended or planned.