Date: 1901. Image courtesy Douglas Yeo
This is a contrabass trombone, which means it is an octave lower than a (regular) bass trombone. Note the double slide. This remarkably well preserved instrument is owned by Douglas Yeo, bass trombonist of the Boston Symphony Orchestra and music director of The New England Brass Band.
Apparently only three of these were made, or at least are known to exist: this one, one that is in the Conn museum, and one owned by Murray Crewe of the Pittsburgh Symphony. Mr. Crewe's instrument was made in 1902, which leads to the conclusion that in all likelyhood this model was made between 1901 and 1902.
Here is an interesting Youtube clip about Mr. Crewe's instrument: A Rare Beast