The problem with bikes is that miles don't always have as much to do with servicing as it does with cars. You can ride for weeks in dry weather and not have to touch anything but then a couple of rides in the winter and it's all covered in horrid corrosive salt. Equally you could do a bit of riding on some dodgy roads and things rattle loose, wheels go out of true etc. I think it's useful, as others have said, to be able to recognise the basic faults - if nothing else it helps when explaining to the LBS what needs doing.
Like you I've always been a technically cack handed but the funny thing about bikes is that they are incredibly crude machines. You'll be surprised how easy it is to go from recognising you need, for example, a new brake cable and asking the LBS to fit it to thinking, 'how hard can it be?' and doing it yourself. Next you'll be indexing gears and it'll only be jobs that need specialist tools that you'll be handing over to the LBS. It's actually enormously satisfying and therapeutic (although that might just be me).
Probably need to get the oil out...that said if it keeps raining I'll need an ark not a bike!! 
