Hey Jack, by coverage uniformity, you effectively mean the variation in read-depth across each base in your regions of interest, right? BEDTools does have a function for calculating per-base read-depth, but you can also calculate mean read-depth across your defined regions of interest. So, 'coverage uniformity' will depend on how you summarise your read-depth in your regions of interest.

If I wanted to look at a coverage profile, I would calculate per-base read-depth and then plot it out on a line graph, and also calculate the variance.

You may want to take a look at this R function: https://www.rdocumentation.org/packages/TEQC/versions/3.12.0/topics/coverage.uniformity

You may also want to take a look here, where the poster has used a package called 'breseq' to generate what I would say are very similar to the graphs that I generate to look at coverage uniformity using base R functions: Non-uniform illumina coverage, why?

htSeqTools has a function to calculate the standardized SD of the genomic coverage. Alfred (disclaimer: our own tool) also calculates such a standardized SD of the genomic coverage. A pre-compiled static binary is available here.