I've never purposefully underbid. If anything, it creates doubt in the value of your service. Why do they need to know that you're starting out? It's frankly none of their business. Not only that, but people only see your lack of experience as leverage to barter you down further and/or attempt take advantage of you.
And when the customers who got you to clean at a GREAT rate refer you to someone based on the dollar amount, or want you to return, are you really going to say "sorry, I'm so popular now that if you want me back I have to charge more this time"? Weird.
In fact the more I charge, the more business I receive. And the better customers I attract. My biggest pain in the ass customers are hyper focused on the cost. My best customers understand the good ol' motto "cheap labour isn't good, and good labour isn't cheap" - they appreciate the work we do and understand why it costs what it does.
I would focus on making your business unique. Stand out more professionally above the competition, use better equipment, do something a little special (we leave tea & chocolate with our thank you notes after every clean), market yourself a little differently. It costs very little and allows you to charge a premium.
ETA: there is no reason why you can't build your reputation WHILE charging more. Anything less is money flushed down the toilet.