Short answer: Never - as virtually every 1200 bps also speaks 300 bps :))
Beside that, it's higlyhighly vague to pick any point in time, as the use of modems deiifered extremediffered extremely over use cases which itself carried vastly different user numbers, so using any total might be distorting.
For example, by 1990, when you got your 300 bsbps modem, I was already using a Trailblazer for 3-4 years. Depending on the connection switched, it's PEP protocollprotocol (*1) sustained data rates of 18 or 19 kbps, depending on the line switched (*2). And all my peers where equipped alike - and ofc, all BBSes we called.
From a development point, 300 bps are around since the 1962 (Bell 103A), the 1200 bps 212A was introduced in 1976. Hayes did introduce therritheir 300 bps Bell 103 compatible Smartmodem in 1981 and a 212 compatible Smartmodem 1200 in 1982. InternaltionalyInternationally these standards wherewere, in conjunction with other, similar ones, layedlaid down as ITU-V.21 and V.22.
So yes, even by only looking at the US, 1200 bps wherewere around in consumer grade-grade devices almost 10 years before you got your modem.
Then again, worldwide (and in the US after 1985) 1200 didn't play a big role at all, as 2400 bps was standardized in 1984 as ITR V22bis (*3). Since Standards take some time to become official, manufacturers already offered V.22bis compatible modems operating at 300, 1200 or 2400 bps line speed. Hayes did so in early 1985. By 1987 the Smartmodem 2400 was the only one offered, and available at or even below 200 USD.
Bottom line, in 1990 aquireingacquiring a 1200 bps modenmodem was only possible second hand, and even then it was like stone age quipmentequipment. Standard was 2400 bps or faster. Not many BBS operators accepted users to occupywho occupied the line 8 times longer than what was considered average.
*1 - A protocollprotocol originally developed for military use in less than goodideal conditions, with an emphasis to get a conectionconnection no matter how disturbed the line is - effectivlyeffectively the base of todaystoday's ADSL, pumping several megabits over classic phone lines :)
*2 - History insert: When in 1989/90 the iron curtain fell, we did help new BBSes popingpopping up in East Germany with Telebit modems, enabelingenabling them to transfer at speeds never below 10 kbps - which is darn good, considering that much of the eastern phone network was basiclybasically pre war-war technology - and often even from backbefore then.
*3 - The suffix bis
denotes a second, extended edition with new features - likewise ter
stands for a third one. Both taken from French, once the official language for telecommunication standards.