Convert boost::bimap to std::map

The obvious way to convert a bimap to std::map, doesnt seem to work. Is below the correct/good way to convert? Is there a better/shorter way?

typedef boost::bimap<int, std::string> MapType;
MapType _bimap;
//Fill _bimap
MapType::left_map& lmap = _bimap.left;
//std::map<int, std::string> bmap(lmap.begin(), lmap.end()); //THIS DOESNT WORK
std::map<int, std::string> bmap;
BOOST_FOREACH(MapType::left_const_reference entry, lmap)
{
   bmap[entry.first] = entry.second;
}