Bear vs. Barney
You can also find Bear DVDs/videos at your public library.  I have watched it with my daughter and will say that it's a million times better than that purple pedophile.
Barney rips off nursery rhymes by changing the lyrics and adding dumbed down/PC lyrics of it's own (His theme song is a version of "This Old Man").  While BITBBH has original songs on every show.  
Barney is a very boring, simple walk around suit voiced by someone other than the puppeteer.  Bear is a puppet similar to Big Bird, with the puppeteer saying his lines while recording the show (the songs are pre-recorded).  There are many other puppet characters in Woodland Valley, each with it's own personality PLUS!  Barney characters are like watching cardboard.  Boring.
Give Bear a try, it's fun and it's smart!