Is it possible to configure pgbouncer to distribute queries among master and slave?
pgBouncer cannot do that, and indeed it is a questionable feature. How can you reliably tell that a statement like

SELECT pg_create_physical_replication_slot('aname');


won't modify your database?

There is pgPool which boasts such a feature, you might investigate it.

The better technique is usually for your application to use two database connections: one for reading and one for data modifications. That doesn't put you at the mercy of a tool that tries to guess.