How can I convince my company to sponsor corporate cycling gear?
The easiest way to do this is centre it around a competition that a contingent of your BUG is competing in.  That way you can pitch around the competition and the exposure.  Even if it is just a big social ride.  

Work out your team.  Work out the cost of the corporate uniforms.  Pitch based on the competition demographics (Hopefully it appeals to your company), also on the fact you have internal participants.  

You won't have gear available for the whole company but this is the easiest starting point.  Then from there you can prove interest and say it is encouraging employee health.  Not sure where you are located but some companies jump on programs like this.

Good Luck.