Bosmer (Wood Elves) have bonus experience for bows, Dunmer (Dark Elves) bonus experience for dual wield. But I wouldn't base any race choice on bonus experience since eventually you'll be max experience in it anyways.

I would instead look at other bonuses, like if Khajiit have a bonus for weapon critical and bonus damage when sneaking. If you're going to focus on stamina builds, which are what Dual Wield and Bow abilities use, then other good choices are Imperial (bonus to max stamina, max health and regain health on melee hits) and Redguard (bonus to max stamina, stamina regen and regain stamina on melee hits