gefärbt
dyed
Provided with color; having received a different color from the original one. Often refers to hair or textiles.
Sie trägt eine Bluse aus blau gefärbter Seide.
She is wearing a blouse made of blue-dyed silk.

dyed / biased
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dyed
Provided with color; having received a different color from the original one. Often refers to hair or textiles.
Sie trägt eine Bluse aus blau gefärbter Seide.
She is wearing a blouse made of blue-dyed silk.

The word 'gefärbt' (dyed) is the past participle of the verb 'färben' (to dye/color). It is used like an adjective to describe a noun that has received color.
Mir gefallen deine frisch gefärbten Haare.
I like your freshly dyed hair.
You can recognize the figurative meaning 'biased' from the context. If 'gefärbt' (biased/colored) refers to abstract nouns like 'Meinung' (opinion), 'Bericht' (report), or 'Darstellung' (account/portrayal), the figurative meaning is intended. With concrete things like 'Haare' (hair) or 'Stoff' (fabric), it is about literal color.
Sein Bericht über den Vorfall war sehr emotional gefärbt.
His report about the incident was very emotionally colored.
In the figurative meaning, 'gefärbt' (biased/colored) is often specified more precisely by an adverb. Common combinations are 'politisch gefärbt' (politically biased), 'emotional gefärbt' (emotionally colored), or 'subjektiv gefärbt' (subjectively biased).
Die Diskussion war leider sehr ideologisch gefärbt.
Unfortunately, the discussion was very ideologically biased.
In the literal meaning, 'gefärbt' (dyed/colored) often describes hair, textiles, or other materials. Typical nouns are 'Haare' (hair), 'Wimpern' (eyelashes), 'Stoff' (fabric), 'Leder' (leather), or 'Glas' (glass).
Die Künstlerin verwendet oft bunt gefärbtes Glas für ihre Fenster.
The artist often uses brightly colored glass for her windows.
colorful
'bunt' and 'gefärbt' can both describe something to do with color. 'bunt' means that something has many different colors or looks colorful. 'gefärbt' means that something has been changed by color, for example hair or fabric. It does not have to be colorful; dyed hair can also be just black or blond. The words can be confused because both are used with color. Remember: 'bunt' describes an appearance with many colors, while 'gefärbt' describes that color has been applied to something or changed.

Nach dem Friseurbesuch sind ihre Haare dunkelrot gefärbt.
After the visit to the hairdresser, her hair is dyed dark red.
Am Wochenende schmücken wir den Raum mit bunten Luftballons.
At the weekend, we decorate the room with colorful balloons.