How can I get bedtools to tell me which genes are being expressed?
Bedtools is not the best tool for this. You can use featureCounts, which gives you the number of read that overlap with features in a genome. In this case, your features are genes.
bedtools coverage is used to calculate the overlap between each read in BAM and each line in BED. It is not very straightforward to quantify gene expression. Plus bedtools does not account for exon in each gene and summarize them to gene level, like featureCounts does.