try a sound recorder- there are loads on the net 'AIPL Singulator' is ok it can capture from any source you can play http://www.aipl.com/singulator.html or better still try audio grabber http://www.audiograbber.com-us.net/ it is free and claims to be able to capture audio from any source!
There are methods for myspace, I don't know about bebo. You'll have to google it, but if you google for myspace you should be able to get songs off that.
I personnally use audacity set to 'What U Hear' to record streaming audio. Completely free, but you'll likely need a codec pack installed to be able to save as MP3 (the NIMO codec pack has the .dll needed).
(Careful when using IE, remember links 'click' when you follow them.)
i am not a beebo member so dont know how they host files, but have you tried looking at the page source code to see if there is a direct link to the audio clip.
I used to do this for ringtones they wanted you to buy, copied the link URL and opened in new tab in Opera and the save dialog box would come up, very simple very easy if you know what to look for.