Short answer: You only activate 1 by paying 1 red mana
Long answer: let's first clear up your vocabulary a little. From your original question, it's unclear if you want to play both enchantments from your hand onto the Grizzly Bear for {R}, or if you want to use the abilities listed on the enchantments. Do you realise enchantments are what we call 'permanents'? Once played, they remain in play until they are destroyed, returned to your hand or, in the case of creature enchantments, the creature they are bound to disappears. You only pay the casting cost when you put an enchantment in play.
Once the enchantments are in play, they grant additional abilities to the creature they are enchanting. In order to use such an ability, you
- declare you want to use an ability (for instance, the 'deals 1 damage to target creature with flying' ability on Dizzying Gaze)
- Pay the cost, choose a target
- Resolve the ability (and perhaps others that were placed on the stack as a reaction to this).
As you can see, all of the above is for one of the extra abilities that your creature has, now that it is enchanted. Same goes for the other ability. When you pay {R}, it is always for one activated ability.