I'm a driver, cyclist and pedestrian.
YABU totally and utterly U. Bikes never belong on the pavement.
If you don't feel confident on the road do a course as others ahve suggested or read Cylclecraft the cyclists bible.
To make your self safe on a bike you have to be visible. Ocassionally that means a precious driver losing 5 minutes on their journey but they would lose considerably more time if they actually knocked you off.
The thing that drivers miss about city cycling is that cyclists take longer to get between traffic lights but because most cars end up waiting at the lights the time taken to travel A-B is actually the same.
I have proved this on a number of occasions. Most spectacularly when one of my neighbours (in a flashy sportscar with equally distinctive personalised plate) carved me up in spectacular and dangerous style at a junction near work.
I recoverd and pedalled on home. When I got there he too was just arriving home. He was quite suprised when I went over and remonstrated with him pointing out that his 'fast' car and potentially life threatening driving had got him home at exactly the same time as my very safe cyclist (metaphorically I cycle a 3 speed granny bike but the locals hills necessitate a road bike).
On another ocassion some tit actually drove at me in heavy traffic as he objected to me 'taking the lane'. After all being one place in front of me in teh queue was vitally important. He was so closed I felt moved to engage with him. We had words. He overtook. I then followed him all the way to work (directly behind him in heavy traffic). He was one of my newly appointed colleagues. I think he was embarrassed. Attempting to killi your colleague on day 2 of the job by driving into them in your BMW is never cool!