Hi Katey, I don't know about buses because I never catch them but the trains in Sydney are fairly easy to use. You don't have the issues of folding and unfolding the pram or bubs needing anywhere to sit. The only problem is if you need to use a station that doesn't have disabled access you have to drag your pram up and down the stairs. If there are two of you its easy but a bit harder for one person. I got a second pram that is much lighter than my usual one for trains because I usually catch them on my own when DH is away with the car. To get it up stairs I usually carry Yasin and drag it, sometimes if I'm near Lakemba and I notice that there are Muslim men nearby I just stand around and look helpless and usually someone will offer to carry it for me. It doesn't seem to work so well on Australians.
For short trips when Yasin was younger and lighter I used to just take him in his sling because it left my hands free and there were no hassles with stairs.
Alot of shopping centres have stroller hire so you can catch the train carrying bubs in your arms or a sling and then borrow a stroller while you shop.
You'll find that you meet lots more old ladies on the train than you used to because they all sit in the bit near the door and want to know all about your baby.
I think that catching public transport with kids is a great idea. It gets them used to not relying on a car and reduces pollution.