If you have a decent genome or transcriptome for B and the genomes/transcriptomes are different enough then sure, align everything against B and then take the unaligned reads and assemble them. Many mappers have an option to write unaligned reads to a separate file, which would be convenient for this.

You could give BBSplit from BBMap suite a try with the genome you have at hand. You are going to have trouble with genes that are shared/homologous with both species. BBSplit allows you multiple options. You can choose to assign the reads to both or collect them in an ambiguous pool that you can look at separately.

Seal.sh from BBMap suite is also able to separate reads based on k-mer profiles. If it helps you may need to be tried out.

You could map the mixed AB reads to B's genome and keep the unaligned reads. This approach is obviously dependent on the stringency of the mapping and the similarity of their genomes...

Here's an example:

bowtie2 --phred33 --very-sensitive --threads 8 --time -a -x B_genome.fa \
-1 AB_R1.fastq -2 AB_R2.fastq \
--un-conc A.fastq \
--al-conc B.fastq \
> /dev/null