I've experimented a bit with bronze age units and movement and found some pretty consistent rules.
If taking the movement value as it stands; grasslands cost 2, hills, bush and forest 3, rock 4 and swamp 6. There is one caveat, might be a bug or a "feature". If you make a partial move and enter a hex from which you will only be able to move one more hex and wouldn't be able to attack after that movement, your unit's turn will end automatically.
This can be tested, for example, by moving a movement 12 unit 5 hex over grassland. Notice that the unit initially( or during the move if you're making multiple partial moves) will be able to cover six hex, but upon entering the fifth hex the units turn will end.
Please comment if you find any inconsistencies using this.
Robertflatt