I play Bass Clarinet for a school band, and may have to buy my own mouthpiece. I'm wondering what the difference in tone quality is between a plastic and rubber mouthpiece, and if a rubber one is more difficult to play?
For all woodwinds, plastic mouthpieces are generally "starters" that come with student clarinets. Professional mouthpieces are usually made of a hard rubber called ebonite.
How difficult the mouthpiece is to play depends entirely on the design and shape of the piece (largely on the tip opening and how that is matched with your reed strength), not on the material. Rubber mouthpieces will have a better tone quality, not affecting playability.
Yamaha does make some plastic mouthpieces that are very consistent and generally accepted for school players, but if you're looking for something of higher quality (and consequently more expensive), try out some Selmer or Vandoren pieces.
If we have any professional bass clarinetists in the audience, I would be interested to hear what is considered "standard" in the profession right now.