Śrīmad-Bhāgavatam 10.39.40
Blended reading (Sanskrit + English inline)
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upāmantrya
—
having taken leave / requested permission
Upa + ā + √mantra — to formally request / invite. Akrūra observes the proper etiquette: even though Kṛṣṇa is his charge, he asks permission before leaving the chariot. Devotee's reverence does not lapse.
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hradam
—
to the deep pool
Hrada = a deep pool (as opposed to shallows). Akrūra goes to the deep part — a hint that this will not be an ordinary ablution but an immersion-encounter. Depth is preparation for darśana.
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vidhi - vat
—
according to scripture / prescribed rules
Vidhi-vat — 'as per vidhi.' Akrūra is a learned man; his bath follows śāstric procedure exactly. The Bhāgavata insists: extraordinary vision comes inside scrupulous ordinary practice, not despite it.
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snānam
—
the bath
Snāna = the prescribed Vedic bath with mantras. Akrūra is performing the same daily snāna any orthodox Yādava would do — yet inside this routine bath he will see all of Vaikuṇṭha. Routine is the site of revelation.
Having Krsna and Balarama sit on the chariot, for their comfort or because of fear of enemies, Akrura when to the Yamuna.
Because of disturbing the minds of the gopīs, Akrūra could not bathe in the great sweetness of Kṛṣṇa as the devatās did. This is explained in three verses. Taking permission from Kṛṣṇa and Balarāma, he took his bath. He kept them on the chariot so that they could sit comfortably. He bathed at Ananta-tīrtha (kālindyā hradam). Instead of hradam sometimes tīram (bank) is seen.
Seeing the two in the chariot, fearing enemies, he took permission and went to a pool of the Yamunā. Or he placed them in the chariot fearing they would go back to Vraja. The pool was a famouns tīrtha. According the rules he bathed. One should offer respects to the tīrtha and do ācamana. This is explained in Padma Purānā, concerning the glories of the Yamunā. This is also written in Bhagavat-bhakti-vilāsa.
Like a brāhmaṇa-uncle who, having seated the prince in the chariot, requests permission to bathe in the river he has been longing to enter — Akrūra invites the two Lords to be seated, takes Their leave, and walks to a deep pool of the Yamunā for scripture-prescribed bathing. He has been waiting for this bath since he left Mathurā.
My note
Source: vedabase.io