It's possible but unfortunately not super straightforward to extract the unmapped reads.

You can use the --num option when mapping reads using kallisto bus.

You then use bustools text -pf on the output.bus file. The read number (zero-indexed) of the mapped reads will be stored in the flags column (i.e. the fifth column). That will tell you which read numbers (zero-indexed) in the input FASTQ files mapped (all other reads are unmapped).

I'll put together a tutorial on how to do this (or perhaps a simpler workflow) at a later date.