To change your city into a transport paradise, you need to get people on bikes and buses, and support people walking.
For buses, you need to stop them getting held up in peak-time traffic queues, using bus lanes or bus gates. Buses need to be good enough to get traffic volumes under control.
For bikes, you need to make direct clear routes on main roads, using cycle lanes. Traffic speed needs to be reduced, by generally only having a single narrow traffic lane in each direction. Pedestrian crossings and tight side road junctions also help. Main road junctions need to be reasonably calm, with advanced stop lines or tight-entry roundabouts.
You also need quiet routes away from the traffic, particularly for younger cyclists, linking schools and shops, and using a mixture of tracks and backstreets. Side roads generally need to be calmed, with parking switched from side to side, and 20mph limits. In-between roads need calming with speed cushions and 20mph limits, and traffic volumes reduced to no more than about 3000 motor vehicles per day.
To encourage walking, you need raised crossings of side roads, so that walking along main roads is uninterrupted. The complexity of crossings at major junctions needs to be kept to a minimum, and there should be no poorly-lit indirect subways.
As you improve provision for bus services, bikes and walking, you will find it practical to restrict car parking and car access, particularly in the city centre. This will give you further opportunities to improve conditions for cycling and walking, and reduce delays to buses.
Implementing this will undoubtedly take some time, but we can review your current transport situation, and advise where the principal problems lie, and where it will be most-effective to start.