Ways to improve rapid string crossings
My teacher started teaching me Bach Partitia 1006 Prelude and Sarasate Introduction and Tarantella in parallel
I realized the two pieces are quite similar in that they both require rapid string crossings
Are there any ways to speed up the string crossing?
Smaller motions. I could be wrong about this but I have found moving slightly away from the bridge to be helpful.
I reckon two thirds of our technique lie
I concur with Raymond. Also use your wrist as much as possible (this is not enough if three strings are involved like in some of the Bach but on two strings you can get away with moving only your wrist)
You might try experimenting with bow hair tightness and playing by just moving your hand vertically as you rapidly move between the strings. Some bows do this better than others, but just the right relationship between stick flexibility and hair tightness seems to enable it.
Use much less bow than you’re probably using right now.
A well-known practice technique is to first practice bowing the two strings together, then just slightly go out of that plane in both directions for a smooth string crossing.
The advice already given about the wrist is good. I’d just add that it helps to pay attention to the right elbow. Make sure it’s not moving up and down more than is necessary. The arm can significantly slow down string crossings if it’s not moving the right way.
When doing fast string changes, the elbow is stable. Otherwise you look like big bird trying to take off. One way to negotiate rapid changes of 3 strings, like that Bach Prelude, is to have the elbow anticipate the change, so that it looks like the elbow is moving in the opposite direction of the string change.