burst forth vs bloom

burst forth is not a noun while bloom is a noun.

Word	Noun	Adjective	Verb	Adverb
burst forth	No	No	Yes	No
bloom	Yes	No	Yes	No

As verbs, bloom is a hypernym of burst forth; that is, bloom is a word with a broader meaning than burst forth:

Other hypernyms of burst forth include blossom, flower.

burst forth (noun)	bloom (noun)
	a powdery deposit on a surface
	reproductive organ of angiosperm plants especially one having showy or colorful parts
	the organic process of bearing flowers
	a rosy color (especially in the cheeks) taken as a sign of good health
	the best time of youth
	the period of greatest prosperity or productivity

burst forth (verb)	bloom (verb)
be unleashed; emerge with violence or noise	produce or yield flowers
come into or as if into flower
jump out from a hiding place and surprise (someone)