Do I attack with Ezreal Dashing and target a unit with Deflect? Do I have to recycle a Rune?

Yes, you must recycle one rune to pay the Deflect cost when Ezreal, Dashing's triggered ability targets a unit with Deflect.

According to Rule 809.1.c, the Deflect keyword functions as: "Spells and abilities an opponent controls that choose me cost an amount of Power equal to [Deflect Value] more to play as an additional cost for each time they choose me."

Because Ezreal's ability ("When I attack... deal damage... to an enemy unit") chooses a target, it triggers the mandatory additional cost imposed by the Deflect keyword on the targeted unit. As established in RiftJudge FAQ #2939, when an attack ability targets a unit with Deflect, the attacker is required to pay that additional cost by recycling a rune.