I work for a digital agency that's been growing rapidly, but still small enough I can see the biz dev process at work.
It's fairly old school, you get known to the vendor, build a relationship, and they include you on the list of people they consider next time they have a brief.
Public RFPs are hard to win and often have a predetermined outcome (eg. If corporate policy dictates open RFP but the individual has their list as above).
There's a lot of work involved in the relationship building, and often you'll take a small tester project that doesn't make much profit but is an investment for building the relationship so the future projects and retainers are sent your way. Larger agencies have entire staffs dedicated to pitching, full time.
An approach that I've seen work well is to take the smaller projects for more prestigious brands, invest time/money into them to build something great, then promote the hell out of the work (awards, case studies, etc). Hard to bootstrap but once you build momentum, the work comes to you. Most small agencies I've worked with rarely bid on public RFPs and do no outbound advertising.
Direct to brand biz dev is really hard work. The alternative is to continue to subcontract for the larger companies that do the direct biz dev, especially if you want to continue to be a hands on tech and not spend your life pitching and networking. There are many dev shops and production agencies that build substantial businesses this way.