I am using ASpli for the first time. I have an experiment with about 50 libraries per group (responders vs non-responders to a treatment). Am I supposed to concatenate all *bam files for each group, and compare those consolidated bam files, OR should I run ASpli of each pair of samples (indeed, there is no pairs in my experiments, experimental and control samples come from different patients).

No, you shouldn't concatenate all of the samples belonging to a particular class. You can specify which class each sample belongs to by creating a targets data frame. ASpli also doesn't required paired samples, so there's no reason to force samples from the two classes to be paired somehow.