Rob Bowman wasn't fired, he was never on staff. That's not how it works with TV directors. You're asked back by the production and contracted for that single episode. If they like your work and you're still available, you keep getting asked back... Afterwards, he worked most steadily on "The X-Files" for years, becoming their go-to director for hire.
That's true for most television directors, although series often have directing producers on staff these days. Bowman held such a position on The X-Files and now has the same function on Castle. Other examples of directors on staff would be Jon Cassar on 24 and Michael Rymer on Battlestar: Galactica.
Having said that, you're absolutely right about Bowman. He was a "director for hire" on Star Trek: The Next Generation, and certainly wasn't fired. That rarely happens on episodic television, since the schedule is over so quickly that it's probably easier to just let a troublesome director finish their work and never hire them again than it is to go to the trouble of firing them.