Attending Mindfully Versus Without Mindfulness In this answer by ven. Yuttadhammo, it is said that depending on the level of concentration and mindfulness of a person, attending to certain states can result in either wakefulness or tiredness. Hence, I wonder: 

Is it the case that strong mindfulness tends to counter unwholesome states merely by observation, and that without mindfulness these states persevere and may worsen? E.g. a person meditating on a bus mindfully will decrease hindrances, whereas a person mindwandering might increase them?

If so, then I ask: 

Does this entail that strong meditative states 'burn' unwholesome states because of a mindfulness absent from daily life?
Ayoniso manasikāra, as such, means “not directing the attention to the roots of things” or “directing
the attention away from the roots of things,” that is, not observing phenomena as they truly are, not noticing that they are impermanent, unsatisfactory and not-self

Yoniso Manasikāra Sampadā Sutta

Yoniso manasikāra as such means “directing the attention to the roots of things,” that is, observing
phenomena as they truly are, as being characterized by impermanence, unsatisfactoriness and not-self.

Yoniso Manasikāra Sampadā Sutta

OP: without mindfulness these states persevere and may worsen?
... As a result, wrong view arises, and when this
become a habit, wrong view is reinforced so that it remains as a latent tendency (anusaya)

Yoniso Manasikāra Sampadā Sutta

OP: a person meditating on a bus mindfully will decrease hindrances, whereas a person mindwandering might increase them?

If you have initial and sustained application this will reduce hindrances. Mindfulness accompanies by initial and sustained application will decrease it.