There is no set database for contaminants. You don't really know if those reads came from E. coli to begin with but they seem have similarity to and are thus mapping to that genome. You may find that reads coming from basic metabolism genes in bacteria will map to multiple bacterial genomes equally well, especially if you are allowing for errors in alignment.
So it's enough to just use one bacterial genome and relax the parameters with my aligner? I've been using Hisat2 with default parameters like so:
hisat2 -p 4 -x db/ecoli_index -1 06_data_not_aligned/illumina/$sample\_R1.not_aligned.fastq.gz -2 06_data_not_aligned/illumina/$sample\_R2.not_aligned.fastq.gz
At some point you should set aside these suspected contaminant reads and go on with the transcriptome you have already put together. You probably have more interesting biology to discover there.
Since a lot of the reads I have mapped to the genome I'm sure a lot of interesting results will come up. However, we want to build a more complete transcriptome to be used in future studies.