Motorcycles are what a huge chunk of Jakarta actually runs on, they thread through gridlock where nothing else moves and get you across the city in a fraction of the time. Renting one is pretty accessible and there are options depending on how comfortable you are on a bike. Worth looking at motorcycle rental in Jakarta here
https://getrentacar.com/en-US/motorcycle-rental/indonesia-jakarta . Good range of bikes available and everything can be sorted out before you even land.