dāmodarādhara-sudhām api gopikānām
bhuṅkte svayaṁ yad avaśiṣṭa-rasaṁ hradinyo
hṛṣyat-tvaco ’śru mumucus taravo yathāryaḥ
This translation is quoted from Śrīla Prabhupāda’s Caitanya-caritāmṛta (Antya-līlā 16.140).
In the guise of releasing flowing sap, the bamboo trees are actually crying tears of ecstasy upon seeing their child become an exalted devotee-flute of the Supreme Personality of Godhead, Śrī Kṛṣṇa.
Sanātana Gosvāmī gives an alternate explanation: The trees are crying because they are unhappy at not being able to play with Kṛṣṇa themselves. One may object that the trees in Vṛndāvana should not lament for that which is impossible for them to obtain, just as a beggar certainly doesn’t lament because he is forbidden to meet the king. But the trees are actually just like intelligent persons who suffer when they cannot obtain the goal of life. Thus the trees are crying because they cannot get the nectar of Kṛṣṇa’s lips.