When I use the bow on my double bass and play staccato notes, should I lift the bow in order to make the duration shorter or not?
Sometimes I lift the bow and sometimes I just 'let go' of the note I hold with my left hand, but I'm not sure which one is the correct way to do it.
There is a difference between "on the string" staccato and "off the string" staccato with a host of subtle variations (such as spiccato, slurred-staccato, martele, and many others.)
The type of staccato you use depends on the context and the sound that either your or someone else is looking for.
I would consult a bass player for the correct way to perform either type of staccato.
I'll be honest: I'm not a double bass player. However, from my observation of those who are, I can say that lifting the bow seems to be 'the done thing'.
A quick Google of 'double bass staccato' gave me this: http://www.talkbass.com/forum/f5/staccato-bowing-579305/
I trust that will be of more use to you.
"Staccato" is a generic musical instruction. For the execution of its intent there is a variety, partly even a continuum of valid techniques on string instruments. Like with fingerings, positions and string choice, picking something that sounds good and does the music justice remains mostly within the responsibility of the player unless you are playing in an orchestral section where first chair will usually pick the right approach to use in concordance with the conductor's wishful thinking.
