Question
How did men address women in Vaiṣṇava/Vedic culture?
Answer

I present here evidence from Śāstra regarding how men address women in Vaiṣṇava/Vedic culture. I will first present the main forms of respectful address, and then give evidence that men also call non-wife women by name in Vedic culture.
1. ‘Bhadre’ is the vocative (direct address) form of bhadrā (masculine bhadra) which means: “blessed, auspicious, fortunate, prosperous, happy, good, gracious, friendly, kind, excellent, fair, beautiful, lovely, pleasant, dear. “Very bhadra” is Su-bhadra.
Here are examples where a man (and one case of a woman) address a non-wife lady as Bhadre. Unless otherwise noted, verses are from the Bhāgavatam.
1.16.19 Dharma addressed Bhūmi as Bhadre. Note, this is Dharma himself speaking!
6.14.45 Queen Kṛtadyuti addressed her child’s nurse as Bhadre.
8.17.19 Kṛṣṇa addressed Aditi as Bhadre.
10.2.7 Kṛṣṇa addressed Yogamāyā as Bhadre
10.4.21 Kaṃsa addressed Devakī as Bhadre, while preaching bona fide philosophy to her.
10.47.28 Uddhava addressed the Gopīs as Bhadrāḥ (plural).
2. The vocative śubhe (from śubhā) is basically a synonym of bhadre. I found one instance in the Bhāgavatam:
10.2.9 Kṛṣṇa addressed Yogamāyā as śubhe
3. Bhāmini means “O radiant/beautiful, honorable woman”. Sati means “good, honest, wise, respectable lady.”
6.17.24 Citraketu addressed Parvati as Bhāmini, and as Sati.
8.9.6 The Asuras addressed Mohinī-mūrti as Sati.
4. The vocative anaghe literally means “O sinless/faultless lady.” Agha means ’sin’ or ‘impurity’ as in Agha-asura. Thus an-agha
10.33.37 Viṣṇu addressed Devakī as anaghe.
10.35.20 The gopīs addressed Yaśodā as anaghe
5. abala means literally “not strong”, a-bala. The feminine is a-balā.
7.2.39 Yamarāja addressed King Suyajña’s widows as abalāḥ, ‘ladies’
6. Devi means “goddess” or “godly woman”.
8.17.20 Viṣṇu addressed Aditi as Devi.
7. Amba can be: a) a mere interjection, like O! in English; b) a title of respect for ladies; c) good woman; or d) mother.
6.18.71 Indra addressed his maternal aunt Diti as amba.
10.2.41 The Devas address Devakī as amba.
8. Mātaḥ (or mātar) is the vocative “O Mother.” Normally, this word is used to addres one’s actual mother, as when Kapila addressed Devahuti. I found two Bhāgavatam verses where a male addressed a lady who is not his actual mother as ‘mother.’ In one case the lady so addressed was the man’s maternal aunt. The other case was a prayer to Lakṣmī Devī, whom Śāstra declares to be the “World Mother.”
I did not find a single case where a man addressed as mother a woman who was not the man’s actual mother, or who was younger than the man, the same age as the man, slightly older than the man, not related to the man as a mother or aunt, or not the ‘World Mother’, Lakṣmī
6.18.76 Indra addressed Diti, his maternal aunt, as mātaḥ, “O mother.”
6.19.6 In the puṃ-savana rite, one should address Lakṣmī Devī as ‘loka-mātar’, “O mother of the world…”
Similarly, in CC 2.9.188, a devotee refers to Lord Rāma’s consort as “World Mother, Great Lakṣmī, Sītā-ṭhākurāni” (jagan-mātā mahā-lakṣmī sītā-ṭhākurāṇi) Thus the Lord’s consort is the Mother of the universe, since the Lord is its Father.
CC 2.3.172 The devotees refer to Śacī Devī, Nimai’s mother, as ’the mother.’ They do not directly address her that way.
9. Courtship. Men who are courting women address them with many flattering, romantic names, and never call the desired lady ‘mother,’ or anything like that.
10.There is one case where a man addresses a non-wife lady as sadhvi — at 1.17.10 Parikṣit addresses the Earth as sadhvi.
CONCLUSION: In the Bhāgavatam, men address their biological mother as ‘mother’, and in one case, the term is used for the speaker’s maternal aunt. It is also a term of address for the Lord’s consort Lakṣmī. I am simply explaining what is in our main Śāstra.
Now I will give evidence of men calling non-wife women by the women’s actual name.
1. 6.17.17 Citraketu called Lord Śiva’s wife Ambike, the vocative of Ambikā, which is her name.
2. Bṛhad-āraṇyaka is the largest and most ancient Upaniṣad. In its book 3, chapters 6 and 8, the great female sage Gargī debates Yājñavalkya, the first teacher of the Śukla Yajur Veda. Yājñavalkya addressed her by her name, Gargī, dozens of times. Prabhupada often quoted verse 3.8.9 of that text, which includes the direct address to Gargī by her name –Ya etad akṣaraṃ gārgi viditvāsmāl lokāt praiti sa brāhmaṇaḥ. “One who departs from this world, O Gargi, having understood the unperishing, that person is a brāhmaṇah.”
3. Other women, such as the lady sage Maitreyi, are also addressed by their name in this ancient Vedic text.
4. Importantly, our Founder-Ācārya, Prabhupada, wrote hundreds of letters to women in which he addressed them by their names, pure and simple.
5. Millions of devotees address the supreme goddess Rādhā by her name. The word Rādhe is the vocative, direct adress to Rādhā. To say, Rādhe! Rādhe is to address Krishna’s consort directly by her name.
CONCLUSION: I am simply reporting what I found in Śāstra, and in Prabhupada’s personal example. It seems that we have no direct evidence from Śāstra that calling women in general ‘mother’, ‘mātājī’ etc is the preferred, normal, default, or obligatory term of address.
With best wishes,
HD Goswami