Hi, by the sound of it, BCSO is not there in the default list of agencies. Have you changed the config files in LSPDFR folder to add this agency? (Don't worry if you don't understand what I'm saying, it takes a while to get used to these stuff)
Also, no matter which station you go to, you should be able to get access to all agencies (at least the default ones like LSPD, LSSD, SAHP, etc.)
You can change the agency via the menu to get the corresponding vehicles and uniforms.
As you can see above, the agency selected in the first menu item is changed and you can select the corresponding outfit from the next row. This snap is from the Downtown Police Station, with the BCSO agency and outfits added.
(Note:- Even if you have EUP installed, you will again need to change the config files to have them reflected while going on duty, so let's save that for later and make sure you can add an agency first)
Now coming to the next part of your question, you generally have to wait for the dispatch calls. There are ambient events as well (that can be turned on or off in the lspdfr.ini file) or by installing other mods that add ambience. I'd suggest, just to get a hang of it, you can try going on duty as a LSPD cop for now and try playing with the default agencies and change them if required.
To add new agency (like the BCSO among others), you might want to go through these documentations already available to understand how the config files actually work:-
1) Using the custom folder
2) Using backup.xml
3) Agency (you can always copy-paste one of the default agencies and change the necessary tags to make it easy)
Also, you can write back here and I will definitely try to help you out if you get stuck.