I don't know if the BB1 has a shuffle mode of any kind and it's not mentioned on the Brennan website but I'm sure an owner will be along shortly to offer more info. I would add that the shuffle options on the B2 are quite limited. You can only shuffle either your entire music collection or, if you create playlists, you can shuffle them.
As you said you were replacing an MP3 player I thought this worth mentioning as the MP3 players I've owned offer a wealth of random/shuffle modes which are sadly missing from the B2.