Shield bashing, even without ANY of the perks that boosts it, can let you murder dragons.
When you shield bash a foe, they recoil a little. Bonk a dragon in the nose with your little shield and they'll recoil too. The recoil animation on a dragon is really freaking long. Long enough for you to get a few free melee hits in. So just keep wailing away and throw in a shield bash every time the recoil animation finishes. Sure you'll get nibbled on from time to time too but not so much that you'll be guzzling health pots.
When you shield bash a foe, they recoil a little. Bonk a dragon in the nose with your little shield and they'll recoil too. The recoil animation on a dragon is really freaking long. Long enough for you to get a few free melee hits in. So just keep wailing away and throw in a shield bash every time the recoil animation finishes. Sure you'll get nibbled on from time to time too but not so much that you'll be guzzling health pots.