I was utilizing Cloud Foundry's Java Operations Library to perform bind requests to a custom service broker. Recently, I changed the implementation of my custom service broker to provide some data in the response to the bind request. The function call to post a bind request does not support retrieving the body of the response, Mono<Void> bind(BindServiceInstanceRequest request). I have looked into the Cloud Foundry's Java Client Library as well, but found the functionality missing as well.
How can I obtain the body of a bind response using the Cloud Foundry's libraries?
The CF Java libraries communicate with Cloud Controller, not with service brokers directly. The CC API documentation specifies the contract between CC and a client (i.e. your app using the CF Java libraries). The service broker API documentation specifies the contract between CC and a service broker.
I changed the implementation of my custom service broker to provide some data in the response to the bind request
What data are you providing in the response? As stated in the service broker API docs, only the listed fields are recognized by CC and all other fields will be ignored. The fields that are listed in the docs are stored internally by CC, not necessarily returned in response to the CC API call. So you can't expect arbitrary fields in your broker's bind response to make it back to a CC API client (Java library or otherwise).
Any data from a service broker that you want to be a available to a CC API client should be added to the credentials field of the broker's bind request. That field is returned all the way out to the CC API client, and is the typical way that bound apps consume bindings.