If mutations are random, why do antibiotics 'cause' resistance?
There are many models for mutation accumulation (Liò and Goldman, 1998). The simplest model (Jukes and Cantor, 1969) assumes mutations to be a Poisson process. With a given mutation rate, the number of mutations accumulated will follow the Poisson distribution.

This basic model has been extended to include non-uniform mutation rate across the genome and different rates for different kinds of mutations. You can check out the link and the works it cites to have a better idea. 

However, the answer to your question does not pertain to how mutations happen. Although there is some evidence that some antibiotic treatment can actually increase mutation rate (Long et al, 2016; Meouche and Dunlop, 2017, Windels et al., 2019), the main principle pertains to selection and not actually the mutations. Improper antibiotic treatment can lead to some cells with moderate resistance to survive, which in turn can evolve strong resistance. Here, we assume that the infecting bacterial pool already has enough variation (or develops during infection) some little resistance. Moreover, there is another phenomenon called persistence (ability to survive antibiotic, Brauner et al., 2016). Windels et al (2019) report that persistence can increase resistance.