Just thinking aloud on the topic here, not speaking from experience. Please feel free to disagree or correct me:
I doubt you can reach the safety levels of, say, the proper car seat. The most likely risks are the drivers who frequently start up with a jolt before you're seated, the need to move toward the door while the bus is still moving, and of course (but less often) the kind of sudden stop or minor crash that sends standing passengers sprawling, in which case of course you don't want to be one of the people standing and casually hanging onto something with one hand (or none), and you don't want to just be holding baby in your arm or arms. You want to be sitting properly, and not in one of the seats with nothing in front of it.
I presume you would want the baby in a carrier strapped to your torso, and if a seat belt compatible with that is available, use it. Some of the seats allow you to brace your feet against the back edge of a wheel well. I imagine that provides more stability.
Try to plan so you do not carry too many things, so that your hands are free to grab onto supports when walking through the bus, and keep your center of gravity low if possible. Try to sit near the door so you can remain seated until the bus actually stops. If you have to stand momentarily (while moving to or from the seat, or waiting for the bus to stop so you can get off), be sure to grab onto supports with both hands (it's amazing how many people don't). Grab fixed objects like seat back or side handles and vertical poles, not the rings that sway, or hold two rings at once so that each is already pulled to its limit, providing more stability.
When on your feet, keep your knees slightly bent and your feet a bit apart, with one a bit forward of you, pointing forward, and another pointing at a side angle, for stability in both directions. I do this all the time when riding the bus and can handle the lurching motion of the bus much better, but I see many people standing with straight, stiff legs and locked knees, feet together. They're more likely than me to be sent flying if the driver really jams on the brakes.
Other than that, I think avoiding the bus is going to be safest; try to use the MRT (with some of the same points applicable there), take the bus only as far as you need to to get to the MRT, etc. As for us, we're shopping for a car so that we can have a properly installed seat for the baby.
Pleasure is spread through the earth In stray gifts to be claimed by whoever shall find. —William Wordsworth