bitter
One of the basic tastes, perceived as sharp and often unpleasant, as with chicory, grapefruits, or black coffee.
Diese Schokolade ist mir zu bitter, ich mag lieber Vollmilch.
This chocolate is too bitter for me; I prefer milk chocolate.

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One of the basic tastes, perceived as sharp and often unpleasant, as with chicory, grapefruits, or black coffee.
Diese Schokolade ist mir zu bitter, ich mag lieber Vollmilch.
This chocolate is too bitter for me; I prefer milk chocolate.

Besides taste, 'bitter' very often describes painful feelings or disappointing events. Typical combinations are 'eine bittere Enttäuschung' (a bitter disappointment), 'eine bittere Niederlage' (a bitter defeat), or 'die bittere Wahrheit' (the bitter truth).
Es war eine bittere Erkenntnis, dass er den Job nicht bekommen würde.
It was a bitter realization that he would not get the job.
In connection with cold, 'bitter' acts as an intensifier and means 'very' or 'extremely'. People speak of 'bitterer Kälte' (bitter cold) or a 'bitterkalten' (bitterly cold) day.
Draußen herrschte eine bittere Kälte.
There was bitter cold outside.
The phrase 'Das ist mein bitterer Ernst' is used to emphasize that you mean something absolutely seriously and that it is not a joke.
Ich kündige meinen Job. Das ist mein bitterer Ernst.
I'm quitting my job. I am deadly serious.
The phrase 'etwas bitter nötig haben' means that you need something very urgently. Here, the word 'bitter' intensifies the urgency.
Nach dieser anstrengenden Woche habe ich ein Wochenende Ruhe bitter nötig.
After this exhausting week, I badly need a quiet weekend.
In the literal sense, 'bitter' is often connected with certain foods and drinks. These include, for example, 'bittere Schokolade' (bitter chocolate), 'bitterer Kaffee' (bitter coffee), or 'bittere Medizin' (bitter medicine).
Manche Salate wie Radicchio haben einen bitteren Geschmack.
Some salads, such as radicchio, have a bitter taste.
urgent / urgently
'dringend' and 'bitter' can overlap in certain expressions when something is very necessary. 'dringend' is the normal word when something is urgent or absolutely needed. You can use it in many situations. 'Bitter' has many other meanings, but in expressions like 'bitter nötig haben' (to badly need), it intensifies the necessity. It sounds stronger and often more emotional than 'dringend'. For clear everyday language, 'dringend' is usually the direct choice. 'Bitter' fits mainly in fixed expressions.

Nach drei Wochen ohne Pause hat das Team einen freien Tag bitter nötig.
After three weeks without a break, the team badly needs a day off.
Vor der Reise brauche ich dringend einen neuen Ausweis.
Before the trip, I urgently need a new ID.