No, it is not particularly bitter.

In an English pub, when one asks for a bitter or an ale or simply a beer (unless one specifically indicates lager, which in the English nomenclature does not count as a beer) the barkeeper will draw a bitter, a running beer that is only moderately alcoholic and, notwithstanding the name, is not bitter.

It is called this way for historical reasons. In the 1930’s the most commonly consumed beer in Great Britain was the “mild,” whose characteristics identified with the name, so with a full but suave flavor. After the Second World War, it was largely replaced by the bitter, which met the new tastes of the period, with a slightly more bitter taste and a color that had changed from brown to light brown. But the two styles, mild and bitter are very similar. Both are little fermented (hence running beers) with a medium-low alcoholic content (ABV 3-4%), which lend themselves to an evening with many glasses among friends, therefore, session beers.

Cheers.