You don't deposit any fiat on Bisq. 
Instead, it's done via an escrow system, with multisig'd security deposits of BTC. 
The fiat transaction happens separately. This way, there is no fiat information outside of the fiat system itself. 

As an example, via Revolut as the fiat payment method you can even pay without any of the peers exchanging any payment info. 
Along with this there is a mediation system. 
Either way, the end-state is that on the fiat-side it looks like a regular TX, with no connection to BTC at all. 

As for requiring BTC beforehand, Bisq has a Matrix room where a tradce for the initial minimum amount for security deposits on the bisq market can take place P2P and mediated by the admins.