Whenever a "bullpen" is referred to here, I know a lot of amateur fields will have no such thing - as compared to what's seen on TV while watching the Majors. In fact, I've seen nothing more than a stretch of grass somewhere behind a park bench, behind the wire-backstop, and even on the edges of a parking lot, sometimes, is the best that one can hope for.
Regardless, you do the best you can with what you got.
The following example is a good study in one pitcher's "working the bullpen." Now this is not an example of how every professional works his time, but good enough to show you some very basic and simple techniques.
Again, some techniques.
Here's what to look for as you watch this:
Notice throughout the video the man's concentration - nothing haphazard about this man and his intent. He's deliberate and in control of what he's trying to accomplish. In fact - at the 2.07 mark in the video, someone makes a remark about something in earshot of the man, and he's not too happy about it.
Watch how he wants his backstop to do certain things. This pitcher is trying to get a point of reference with his intent at his target(s), noticing any control issues, and so on. His backstop starts to move to one side - at the .36 mark in the video, BUT, this pitcher brings him right back to where he wants him.
Study the place where this pitcher starts in relation to the backstop, then notice throughout the video he moves from left to right - thus changing the attitude of his pitch, the incoming influence to the backstop, the pitch itself that he's working with while doing all that.
Watch his pitching hand's grip in the glove. This pitcher is working on every detail of his work. He has the glove pocket facing him so he's sure of the grip that he's using to start his experience right. Can you pickup the grip that he's using from the set position? Some pitchers prefer certain pitches from the windup Vs the set position, and the other way around. Not all mind you - just some.
Finally, a little humor to this. After watching the man do his thing in the bullpen ... go back and watch from the beginning the two men standing next to this man's backstop - about 60 feet away. One is in catcher's gear, the other is another staff coach. Watch the antics that those to go through while this pitcher is trying to concentrate and work. It's hilarious. Also, as a side note, sometimes a pitcher in the professional game can get really full of himself. To loosen things up, a couple of players and even a coach will post themselves, like the two in the video, and get very imaginative with the antics ... I did.