I am looking for a hypernym of to deposit and to withdraw (money to and from a bank account).
I thought about several options like "to perform a financial transaction", however I need something more concise and short.
The first hypernym I thought of was transaction, which can be a hypernym for deposit and withdrawal.
You're looking for a verb, though, not a noun. That being the case, you could use the verb transact. Wiktionary says:
transact (v.) 1. To do, carry through, conduct or perform some action. 2. To carry over, hand over or transfer something. 3. To conduct business. 4. To exchange or trade, as of ideas, money, goods, etc.
Transfer can be used as a noun or verb to refer to deposits and withdrawals.
Use transfer. This goes both ways.
I transferred money to my account.
I transferred money from my account.