Bb doesn't "require" you to play in G capoed up. You can play in Bb without a capo if you want. It's just that the chords in Bb are less than ideal on a guitar in standard tuning. So by placing the capo somewhere on the neck you can still play in Bb but use the chord forms of another key that is more desireable. You aren't playing in the key of G, you are playing in the key of Bb using chord forms from the key of G.
With the capo on the third fret your open E becomes an open G. Then forming a G chord over that you will notice that the bottom note in the chord is a Bb. So you are playing a Bb chord using a G form. Similarly if you left the capo at the third fret and played using chord forms from the key of C you would actually be playing in the key of Eb. If you used chord forms from the key of D you would be playing in the key of F.
Prove it to yourself by playing a G chord form with the capo at the third fret and compare that to a Bb chord without the capo. Try the same with the C form with the capo and note the comparison to an Eb without the capo (you can fake the Eb by playing just the top three strings of a standard D chord all raised one fret) and then a D chord form compared to an F without the capo.
From there try the capo at different locations using those same basic chords and see if you can figure out what chord you are actually playing. A piano might be helpful here to match tones if you don't know the note positions on the fretboard.
Hope that helps a little. Capos are wonderful devices.
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