I was in a similar position, type of bass (cheap) and a very high action out of the factory, I removed a string at a time to preserve the sound post, filed each notch in turn to my required height at the bottom of the fingerboard then onto the next. When each string was at the required height I then removed the bridge, keeping weight on the sound post, and removed the waste wood, smoothed the notches and added graphite.
The whole process was straightforward and very successful taking my heights to 7 - 10mm G to E.
I have also used 3mm bendy ply pads to raise the bridge, as the name suggests it is very flexible and "moulds" to the body shape keeping the integrity of the bridge feet without the need to sand.
Whilst not at a luthiers standard it all went well and gave the desired result total cost £1.00 for the A4 size sheet of ply.