There might be a patch available for this already. In the worst case articulated above (less than 64 columns), if all the nulls are trailing nulls, the bitmap need not be saved. Actually it is not 64(actually 72), as postgres heaptupleheader is only 23 bytes and one byte is left for the start of the bitmap.
The same principle can be considered for Index Tuple as an extension
Thanks,
Gokul.