Transformation underpins a lot of lab modern projects.
This will be a very unsatisfying answer, and this wikipedia entry explains why. The time, and success, of bacterial transformation of competent cells varies greatly depending on a few things mainly:
- the length of nucleic acid sequence for insertion (or more accurately, the plasmid)
- the species of target organism (or more accurately, the genotype of the target organism)
- a host of other things
With a specific plasmid and organism you would be able to get a more satisfying answer, but I imagine the answer would even differ from lab to lab.
I worked with a microbiologist that provided me with a protein as a part of my honours project, and I can give you a broad impression I got from them: it does not happen often. Sometimes none of the cultures you are trying to transform will incorporate the new sequence into their genome, other times the cloning process goes very well and all your cultures will be transformed successfully. For our project, valid colonies only presented after a week with reasonable success (more than half the attempts were successful). But you don't know if the transformation worked until way after the first transformation happened.
The mechanisms behind this are grossly understudied. If we take some thing B. subtilis, arguably the most academically studied organism in the field of transformation, it can take up the DNA as food or incorporate it into its genome but nobody knows exactly how this happens at a molecular level (Chen & Dubnau, 2004)
Chen, I., & Dubnau, D. (2004). DNA uptake during bacterial transformation. Nature Reviews. Microbiology, 2(3), 241–9