From May, 2006, to April, 2009, Bob Dylan played DJ on Sirius XM Radio, hosting a show called Theme Time Radio Hour. In this one-hour show, Dylan would select a theme, such as weather, smoking, time, guns, or danger, and play a selection of songs related to that theme. The songs reflected his interest in old-time music: blues, folk, R&B, country, and Frank Sinatra-type crooning.
Dylan also read poems, made jokes, and answered listener emails (though most of theme were fictitious). He didn’t record his segments in a studio; apparently, he would do this in his home(s) and while touring, but when stitched together, each show sounds like a coherent whole.
You can listen to all these shows on the Theme Time Radio Archive website. The episodes are listed in order, with notes, and you can stream them, or download them (right-click on a player widget to download a file). This is a very attractive website, well organized, with lots of interesting content about the shows. Listen in order, or pick one at random; you’ll hear an hour’s worth of interesting music, selected by Bob Dylan, with his take on the musicians or the circumstances of the writing of the songs.