1 kHz sounds moderate and should work with slow 1N4001 rectifiers. I guess, VCC may be too low, only slightly above low voltage lockout level. Both voltage levels have a lockout feature, but the boostrap voltage is at least lower by a diode voltage drop, so it will usually trigger first. You should also consider, that a load connected to the bootstrap supply and high side gate nodes will discharge the bootstrap capacitor. And the high side driver doesn't work, if the low side isn't switching concurrently.