Is there a hypernym for "expense" and "income"?

In a ledger they would be entries.
https://en.wikipedia.org/wiki/Debits_and_credits

In a bank statement they would be transactions.

The bank statement records your transactions debit, credit, deposit, withdrawal.

^{New Oxford American Dictionary (Thesaurus)}

In accountancy there is a common phrase 'income and expenditure' but that's not the single word you asked for.

You might find the term 'cashflow' covers what you intended. Be careful of using that word when speaking with financial professionals though, because they may possibly interpret it with a specific meaning that is outside of your usage.

For your application, postive cashflow would be money coming in (income) and negative cashflow money going out (expenditure).

Broadly speaking, in a business context cashflow will be the instantaneous sum of income and expenditure so you would hear someone say 'we have a month of heavy negative cashflow ahead of us' meaning that in aggregate, they expect their cash resources to be significantly reduced at the end of the period.

In banking terms this would be a Transaction (it's overloaded in software industry but in the Financial Industry it's well defined

Definition: A transaction is a business event that has a monetary impact on an entity's financial statements, and is recorded as an entry in its accounting records. Examples of transactions are as follows:

• Paying a supplier for services rendered or goods delivered.
• Paying a seller with cash and a note in order to obtain ownership of a property formerly owned by the seller.
• Paying an employee for hours worked.
• Receiving payment from a customer in exchange for goods or services delivered.