A beer where you take a sip, and you think, "Oh my, that is weird! But I'll have another sip because it tastes good now", kind of beer?
For really bitter, a double/imperial IPA is the way to go. For the big bitter hop flavors, check out some of these: Stone Ruination IPA, Port Mongo IPA, Russian River Pliny the Elder, Lagunitas (pretty much any of their hoppy beers), Southern Tier 2XIPA, Cigar City Jai Alai. Many more to choose from depending on your location. Maine Beer Company and Kane Brewing are two of my favorite small breweries on the east coast.
As Pepi mentioned, sour beers are certainly very interesting. A great start into the world of sours would be the Oud Bruins -> Monks Flemish Sour Ale, Rodenbach Grand Cru, or Liefman's Goudenband. These will run your a little more $$ but are super refreshing and really great to sip on. They open up and change flavor that longer you leave them out.
There are examples of sour beers where the brewery will suggest taking several sips to get over the initial shock of sourness, so your palette can adjust, allowing you to taste the other flavors. Such beers may or not be bitter (from hops).
In the case of bitterness from hops, I think it takes more than a few sips to desensitize yourself, but maybe that's just me.
How about a beer with German Tradition in it.
IT is called "Tannenzäpfe" which translates to a small pinecone from a fir