Hello there! There are a couple options for what you are trying to accomplish.
It took me so long to write this, 2 other people replied, but w/e.

Short answer to 1): type @nextmap if you are above level 20 and the response will come through global chat instead of a PM.
Long, more informative answer to 1):
1. The !nextmap command actually can be issued using the 'loud' or 'big' command prefix. If you look in /path/to/your/b3/b3/conf/plugin_admin.xml, you will see a line like this:
<set name="command_prefix_loud">@</set>
.
This will determine what character is used for the 'loud' command prefix. You may change it if you'd like. When issuing some commands (such as nextmap), you can use the loud prefix to have the B3 response sent to the global chat instead of being private messaged back to you. With the prefix set to "@", typing @nextmap will give you the result you are looking for. The next setting down in the config file is the 'big' prefix. If you start a command with that, depending on the game, it will bigtext the response to the whole server.
Now look down a couple lines in your plugin_admin.xml, you will see
<set name="admins_level">20</set>
. This tells B3 what level you consider to be someone of admin or moderator status on your server. Keep in mind that a player has to be at or above this level to issue a command with either the 'loud' or 'big' command prefix.
However if you want everyone who has access to the !nextmap command to be able to have the response appear in the global chat, you could edit /path/to/your/b3/b3/plugins/admin.py. If you open that up, search for "cmd_nextmap", look a few lines down and change
cmd.sayLoudOrPM(client, '^7Next Map: ^2%s' % mapname)
to
self.console.say( '^7Next Map: ^2%s' % mapname)
. If you do this, I recommend backing up your admin.py file first. After editing this file, you must restart B3 for the changes to take effect.
Answer to 2):
If you are looking to hide the commands you are executing from the rest of the server, you can PM them to yourself in Quake based games. To do so, type /tell <your name or client number> !command.