Bit map or Bit Vector is used for keeping track of all those blocks which are free. A bit is stored for each block, if the bit value is '0', that indicates that the block is allocated to some process. If the bit value is '1', it means that the block is allocated to some process.
Here in your problem we can see that no.of blocks =768MB/384B= 2^21 blocks. If we are setting 1 bit for 1 block, then it will be 2^21 bits, so it will be 2^18 Bytes, that will be equal to 256KB.