Bowing Off The String
The style of letting the bow jump off the string made popular by Mendelssohn in his "Midsummer Night's Dream", allowing him to explore the character of the scherzo's dancing fairies, which was difficult to express with the normal 'on the string style' of playing. Mendelssohn was one of the first people to make the 'off the string' style of playing popular in serious western classical music. What flowed from that was more use of the bouncy stroke among players, particularly for accompnimental passages.
This chain of notes played by David in the film above would be written with each note having a dot and a slur over the group. However, this making was almost never indicated by composers in the 19th Century, but is a decision taken by players.
The 'off the string stroke' can be started with the bow in the air, or with the bow already on the string for the first note. The advantage of the latter, with the bow starting on the string is that it's much easier for string players to get that together, whereas when starting from off the string is a bit more "chancy".
The problem with starting with the bow in the air when you are playing 'off the string' is the difficulty of getting a large group of string players to get that absolutely, precisely together, which is why in most cases the string stroke is played with the bow starting on the string.
The most commonly used type of bouncing stroke is Sautee, which is the same word as sautee-ing in cooking, when you let the food jump in the pan, like the bow is allowed to jump, not made to jump. IN the film above you can see the fingers of David's right hand (bow) are very relaxed.
The technique of bouncing the bow is rather like that of bouncing a ball on the ground, so when David throws the bow at the string, it just goes on bouncing in an uncontrolled way. The technique is to 'catch' the bow in the fingers in order to control each bounce.
The musical example in the film above is from Rossini's William Tell Overture. David collects the bounces that come as he throws the bow at the string and he just takes two of them and then follows them with an 'up-bow', therefore completing the phrase.