Ask HN: How should we approach our client for an investment?

I'm a co-founder/developer at a bootstrapping Web development company. We're going on two years now and have a steady client base. We think we have a great idea, but we believe the project deserves our complete attention.

We're considering the idea of asking our largest client for a small (~6k) investment in exchange for equity. The investment will cover our living and business expenses while we execute the idea. The client loves us, and we've got a great history working together. It helps a lot that they have connections in the industry we're targeting. But we would rather not "drop a bomb" on them.

We have a meeting this Wednesday to catch up and to discuss future work. What do you think? How should we ask them for an investment?