When did the treble and bass clefs used together become common practice for music notation?
There is a fairly good correlation between the standardization on treble and bass clefs, the standardization of the compass of keyboard instruments at 5 octaves symmetrically about middle C (i.e. F to F or G to G, not C to C as with most modern 5-octave keyboards), and the growth of the music printing and publishing industry.
16th century keyboard music was often written on two 6-line staves, not five. Originally the two staves corresponded exactly to the player's two hands, and C or F clefs could appear on any staff line to minimize the number of leger lines required. Clefs were often changed for each new system of the score, and a visual indication (or "custos") was used to duplicate a note at the end of one system and the start of the next, as a warning of the frequent clef changes.
As keyboard technique developed, avoiding leger lines and keeping a strict correspondence between the hands and the staves became less practical, and the number of staff lines reduced from 6 to 5 with more use of leger lines. However the use of C clefs (on any staff line) remained common.
When the standard compass of the keyboard increased from about 4 octaves to 5, and the whole of the compass was being used by both hands of the player, the modern treble and bass clefs covered the whole compass with only 3 or 4 leger lines above and below the grand staff, and most music was notated that way.
The more widespread use of music printing (rather than hand copying) in the second half of the 18th century probably also increased the amount of standardization - compared with hand copying, engraving the plates for printing music required more "advance planning" of the layout of the complete publication before actually engraving the music, and that was simplified by greater standardization of the notation used.
By about 1780, the use of C clefs for keyboard parts had virtually disappeared.
As the compass of the piano began to increase beyond 5 octaves (from about 1800 onwards) the notation was extended using 8va lines to show that notes should be played an octave higher (and more rarely, an octave lower) than written, rather than inventing new clefs.