Chrissa
The rules seem daft in the sort of situation you're in, but you do have to notify any increase in income. Then what happens is that they re-assess whether you have a "surplus" of £20 per month or more - i.e. your income is £20 or more greater than your reasonable expenditure. If it is, then they can set up an income payments agreement for you to pay that surplus. This agreement runs for 3 years from the date it starts. However, it may be that your "reasonable expenditure" is at present below the figure they allow & in that case they would be less likely to insist on making a payments agreement.
If you do a bit of invigilating then your income goes up for that month, & then goes down again so you might find you had all this rigmarole just to make one or two payments, because the payments agreement would be revised to a nil payment when your income went down again.
However, if the extra income is as little as you say & you have extra expenses related to doing the work you might be OK. You could ring the OR and ask about the possibility & see what they say - you are not then obliged to do any work; they can't make you do it. But make sure you can quote them the amount you will earn & amount of extra expenses etc.
I very much doubt whether your bank account is being monitored, & as sure as can be that you are not under surveillance. They just don't have resources to do this sort of thing unless the case is one where their suspicions are aroused that the bankrupt is attempting to defraud the creditors by hiding assets etc.