Here ओशो-राम-राज्य-कैसा-था Osho is claiming that there was slavery in the Rama's time and women were bought and sold. Are there any verses that mention the same or any proof that there was slavery during Ram Rajya.
If you consider gifting people to brāhmaṇas as if they were one's property, as slavery, then both Rāma and Bharata engaged in slavery.
In Vālmīki Rāmāyaṇa (Ayodhyā kāṇḍa), Rāma instructs Lakṣmaṇa to gift slave-girls (dāsī's) to a brāhmaṇa:
kausalyām ca yāaśīrbhir bhaktaḥ paryupatiṣṭhati |
ācāryaḥ taittirīyāṇām abhirūpaḥ ca vedavit || 2-32-15
tasya yānam ca dāsīḥ ca saumitre sampradāpaya |
kauśeyāni ca vastrāṇi yāvat tuṣyati sa dvijaḥ || 2-32-16
15-16. saumitre = Oh; lakshmana! yaH = which brahmana; taithiriiyaNaam = studying Taittiriya ( a schoolf yajurveda); aachaaryaH = a preceptor; abhiruupashcha = a man of conformity; vedavit = a knower of Vedas; paryupatishhTati = seving; kausalyaam = Kausalya; bhaktaH = with his blessing; tasya = to him; sampradaapaya = in duly gifted; yaanamcha = conveyance; daasiishcha =
servant-maidsslave-girls; kaushayaani vastraaNicha = silken clothes; yaavat = till; saH dvijaH = that brahmana; tushhyati = gets satisfied.
Oh, Lakshmana! Which brahman is studying Taittiriya (a school of yajurveda), a preceptor, a man of conformity; a knower of Vedas, serving Kausalya with his devotion and blessing, to him see that he is duly gifted conveyance,
servant maidsslave-girls and silken clothing till he gets satisfied.
Bharata also donates male and female slaves (dāsī dāsam ca) to brāhmaṇas:
2. On the occasion of Shraddha rites, Bharata gave precious stones, money, a lot of cooked rice, very valuable clothes and various other kinds of presents to Brahmans.
bāstikam bahu śuklam ca gāḥ ca api śataśaḥ tathā |
dāsī dāsam ca yānam ca veśmāni sumahānti ca || 2-77-3
brāhmaṇebhyo dadau putraḥ rājñaḥ tasya aurdhvadaihikam |
tasya = in that; ourdhvadehikam = ceremony performed in honor of the dead; raajN^aH = king; putraH = Bharata the son of Dasaratha; dadou = gave; bahu = many; shuklam = white; baastikam = multitudes of goats; tathaa = and; shatashaH = hundreds of ; gaashchaapi = cows; daasii daasamcha =
servants and servant maidsfemale and male slaves; yaanaamcha = vehicles; sumahaanti = and very big; veshmaanicha = houses; braahmaNebhyaH = to brahmans.
3. In that ceremony performed in honor of the dead king, Bharata the son of Dasaratha gave multitudes of white goats, hundreds of cows,
servants and servant maidsfemale and male slaves, vehicles and very big houses to Brahmans.
Note the difference between the terms 'dāsa/dāsī' (slaves) and 'preṣya/bhṛta' (servants who work for wages) as used in Rāmāyaṇa itself. One cannot simply give away hired servants/maids to anyone they like because they do not own them. Also, unlike servants, slaves cannot afford to get angry with their owners.
प्रेष्य (preṣya) = servant
saṃgrāmātpunarāgamya kuṅjareṇa rathena vā || 2-2-37
paurān svajanavannityam kuśalaṃ paripṛcchati |
putreṣvagniṣu dāreṣu preṣyaśiṣyagaṇeṣu ca || 2-2-38
nikhilenānupūrvyācca pitā putrānivaurasān |
37-38. punaH aagatya = After returning; sangraamaat = from battle; kuN^jareNa = on elephant; rathena vaa = or chariot; paripR^ichchhati = inquires; kushalam = well being of; pauraan = citizens; svajanavat = like relatives; pitaa = father; aurasaan putraaniva = like to their hereditary sons; putreshhu = about sons; agnishhu = about the fire; daareshhu = about the wives; preshhya sishhyagaNeshhu cha = about the servants and the disciples; nityam = always; nikhilena = completely; anupuurvyaachcha = and as per due order.
After returning from battle, Rama goes to citizens on an elephant or a chariot and inquires about their well being as though they were his own kinsmen, like a father does to his sons. He asks about their wives and children, about the sacred fires, about their servants and students, always completely as per the due order.
भृत (bhṛta) = attendant or servant
भृतक (bhṛtaka) = hired or paid
kāla atikramaṇe hy eva bhakta vetanayor bhṛtāḥ |
bhartuḥ kupyanti duṣyanti so anarthaḥ sumahān smṛtaḥ || 2-100-33
33. kaalaatikramaNaat = (when) there is delay; bhaktavetanayoH = in giving bread and wages; bhR^itaaH = the servants; kupyanti = become incensed; bhartuH = against their master; duSyanti = and become corrupt; saH = (and) that; smR^itaaH = is said to be; sumahaan = a great; anarthaH = unfortunate occurrence.
When there is delay in giving bread and wages, the servants become incensed against their master and become corrupt; and that is said to be a great unfortunate occurrence.