Actually bikes are allowed on M2, but bikes must be complaint with M2 requirements,
1 - First it must be at least 500cc in normal routine days and on 23March, 14 august it is lowered to atleat 400cc category, this is a mandatory rule, becuase below thiss bikes are not very high speed and are humble machine to work only in city limits.
You can easy get hit from rear by a speeding 120kmh corrolla or any car, if on even CG 125, because it canot go any more then 105kmh and that is only for a bunch of a minutes then you have to slow down or the engine will sieaze.
2 - Riding on M2 requires special License from M2 authorities Office : KalaShaKaku interchange for free, its an experience apart riding on M2 I have used M2 frequently when I had GS500e, which is now Rulfat darling bike, one must try riding M2 specially if there are two rider on two rides... wow.
3 - Special gear and riding kit is mandatory and listed in your license , and must be weared before hitting in M2,
4 - no fees or toll is required for bike to ride on M2.