I am trying to get the following WFS GET request to work:
But when I add a cql_filter with the bbox filter I then get this error:
Error:bbox and cql_filter both specified but are mutually exclusive
That is correct, the WFS specification says that the various shorthand filter KVPs are mutually exclusive, cannot be used in conjuction.
The good news is that you can encode the whole filter can be expressed as a single CQL_FILTER expression, see some docs here: http://docs.geoserver.org/latest/en/user/tutorials/cql/cql_tutorial.html#geometric-filters
As an alternative, you can also do the same using the FILTER parameter and using the XML OGC Filter encoding.