Does Brush give Ivern, Friend to All an additional +1 from having the tag Ivern and the tag Bird?

No, Ivern, Friend to All does not receive an additional +1 Might from the Brush battlefield token for having both the "Ivern" and "Bird" tags.

According to Rule 184.8, the Brush battlefield token provides: "Bird, Cat, Dog, Poro, and Ivern units here have +1 [M]".

This effect checks if a unit has any of those tags. If a unit has one or more of those tags, it receives +1 Might. Because the effect is not cumulative based on the number of matching tags a single unit possesses, a unit with both the "Ivern" and "Bird" tags still only receives a single +1 Might bonus from the Brush.