You don't have to provide bank details. There are many options for trading Fiat and using banks are only some of the options. However, bank services are the most popular options.

For more anonymous methods, a US Money Order, Amazon gift cards or cash in-person.

Even if you decide to use a bank, the bank doesn't know you're using Bisq or even buying BTC. It just appears as a P2P transfer to/from another individual's bank account. Nothing inherently suspicious about that.