LEAD: There was a time when Mary Pope Osborne was typing in the closet.

There was a time when Mary Pope Osborne was typing in the closet.

After writing at coffee shop counters, J. Timothy Hunt enrolled in a class at New York University, just so he could use the student library.

Ted Bent tried writing at home until a drummer moved into the apartment below him.

Then they discovered the Writers Room. At 153 Waverly Place in Greenwich Village, it is something of an urban writers colony, where writers can come to write their plays, poetry, fiction - even librettos -without being disturbed, and without paying a fortune. This year, the Writers Room turns 10 years old. Roots in the Library

The Room, as it is called by its alumni, was born in 1978 by a group of writers who had been using the Frederick Lewis Allen Room at the New York Public Library, and wanted a space they could call their own. In 1979, the first Room consisted of 11 desks on West 40th Street, after which it moved to a 20-cubicle space in Times Square in 1981, and finally, to its current home on the fifth floor of the Heptagon Building, in 1985.

Most writers tap their typewriters (or computers) in the ''bull pen'' -the adopted name for the main room, with 30 partitioned desks and no talking allowed. A three-month membership costs $150, with an option to renew each quarter. The room is currently shared by about 60 writers, or ''floaters,'' who alternate shifts.

Writers seeking more stability can apply for 1 of the 12 permanent desks - exclusively their own - generally used by writers working on long-term projects or under deadline.

Or, if they prefer complete privacy with a closed door, writers can rent one of the Room's six private offices, at $200 a month. E. M. Broner, the author of ''A Weave of Women,'' said an office accommodated...