LED filament bulb driver
You could consider a circuit like this one (one for each string, plus a bridge/capacitor to make +300VDC): 







simulate this circuit &ndash; Schematic created using CircuitLab

M1 will have to be rated appropriately and have an appropriate heatsink, perhaps of a type typically used in off-line switchers. 

Or see if two resistors (one per string) plus the bridge + capacitor is good enough, because that will be cheaper and more reliable while using the same amount of power.