I second commenter Devon Ryan's suggestion, I'm just going to give a little more detail about how to do that. You can plug the BED files into the UCSC browser following these instructions: https://genome.ucsc.edu/goldenPath/help/customTrack.html
Now you can look at the overlap between your bed tracks (black boxes I believe) and conservation (red box).
Assuming that is all you want to do, that should do it. If you want to do further data analysis or processing, you can download the conservation track as a BED
.wib file from UCSC. You can convert this file to BED as described here, and use BEDTools to analyze it together with your BED of regions of interest.