Some of the challenges you might run into when implementing SLM is, not surprisingly, figuring out why you need it, and who should drive it. Now if we generalize a bit, taking the bottom up approach usually lands you in the IT Ops organization, digging into technical details around up-time, availability, response times and MTTR for applications and infrastructure. Doing it top-down takes you to the business people, who might think about similar metrics, but for services. This has been known to cause confusion and paralysis by analysis.
One way of dealing with this is to let the technical organization define their technical service catalog, filling it with technical service components without worrying about the business side of things. Additionally, it's important to help the business people define the business catalog with business services, without worrying about how those services are supported or delivered, CMDB's, monitoring, technical data, etcetera.
Then the work you just cut out for yourself will revolve around how your technical services build your business services. You'll need some business analysis skills and you probably won't get it right the first time, or the second, but you will learn by each step. And while you're learning, both Service Catalogs will still support both IT Operation and Business.
In the process, you will create a Business Model for IT, which will enable you to understand price, cost and consumption as well as quality.

So in order to create that bridge between IT and the Business, you need to look at it from both sides. But if you can locate who's hurting, start there. Worry about the bigger picture later, and don't try to cram a square peg into a round hole.