Short answer: Never - as virtually every 1200 bps also speaks 300 bps :))
Beside that, it's highly vague to pick any point in time, as the use of modems differed 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 bps modem, I was already using a Trailblazer for 3-4 years. Depending on the connection switched, it's PEP protocol (*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 their 300 bps Bell 103 compatible Smartmodem in 1981 and a 212 compatible Smartmodem 1200 in 1982. Internationally these standards were, in conjunction with other, similar ones, laid down as ITU-V.21 and V.22.
So yes, even by only looking at the US, 1200 bps were around in consumer-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 acquiring a 1200 bps modem was only possible second hand, and even then it was like stone age equipment. Standard was 2400 bps or faster. Not many BBS operators accepted users who occupied the line 8 times longer than what was considered average.
*1 - A protocol originally developed for military use in less than ideal conditions, with an emphasis to get a connection no matter how disturbed the line is - effectively the base of today'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 popping up in East Germany with Telebit modems, enabling them to transfer at speeds never below 10 kbps - which is darn good, considering that much of the eastern phone network was basically pre-war technology - and often even from before 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.