You certainly don't needto do xhost +. That would only help if gvim was running on the remote server and connecting back to X on your workstation. The whole point of bcvi is to avoid forwarding X (and requiring gvim and X libraries on the server). Instead, bcvi uses a forwarded socket to pass one message back to your workstation which then invokes gvim with an scp-style file path.
If you type bcvi filename on the server and get Can't connect to 'localhost:10019' then that suggests perhaps the SSH daemon on the server has been configured to refuse TCP forwarding requests. You can find out for sure by running a command like this to connect to the server:
ssh -v -R 10019:localhost:10019 servername
The '-v' will mean you get a lot of debugging output which ought to include a line like this:
debug1: remote forward success for: listen 10019, connect localhost:10
+019
but in your case there may be an error indicating that the 'remote forward' was not successful. The fix would be to make sure the sshd_config on the server includes:
AllowTcpForwarding yes
Even if you can't make bcvi work, you should still be able to edit a remote file like this:
gvim scp://server//path/to/some/file
|