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Bows have been pretty weak, but in a couple of months they'll get stronger with the patch coming with Summerset. Bows are going to count as two set pieces starting with that patch, which means you'll be able to have two 5-piece armor sets and one 2-piece monster set, and get full use of all of that even with your bow. It'll mean a damage boost for bow and staff users.
So you could train your bow now, and by the time Summerset hits, your character will be ready for it.
Bow offers some nice utility options, and the range can be very useful for a stam build in situations where you need to stay away from the boss.
I'd still recommend running DW or 2h on your other bar, instead of going bow/bow, for the increased damage and the greater flexibility of skills. Also, as others have pointed out, Summerset will open up more build options, because you'll be able to run a full 5/5/2 build with a bow (currently this requires DW.)
As for the race, Bosmers are the first pick for a bow focused build, as they do gain XP on that skill line faster, getting you to abilities like Endless Hail and Poison Arrow sooner. In the long term, that ability washes out, but it can be helpful for you to get started.
Personally, I like using my Bosmer for infiltration, but that's not mandatory.
I have a Bosmer that uses dual wield daggers on one bar, and a bow on the other. It's a great combo. She's a stamina nightblade and rocks my socks off. Sometimes I'll go into stealth and shoot something with the bow first using Snipe (the only good use for Snipe in my opinion), then switch to the daggers and jump at them. She kills fast. (PvE, not PvP.)
If run range only in a group try put everything in stamina and use the spider web synergy skill since that has got range 28 meters of it and get black widow morph.
NA-Xbox one- Ebonheart Pact- Nord Tank DK
PC-NA Ebonheart Pact Nord Stam Templar
Do not listen to all the meta runners. Bowdens are phenomenal. You do -not- need dual wielding. You are on the right track. Boomer is the bow race. You can reach 35k dps atm, and far more soon with the summerset expansion. Flow against the current , not with it.
Warden is the only class that Bow Bow feels good, they have ranged stamina skills and bosmer is the best race for it.
I am hopping for a buff to Arrow Spray in summerset its really underwhelming but its the asylum weapon skill. just doesn't do a lot of damage for its stamina cost.
Sent you a PM. If you're interested in PvP, there's a really strong bow build for ganking that can 1 shot even most tanks. Lemme know if that's what you want. As far as PvE goes... I can help too but personally not a fan