Does Bullet Chess show your real chess ??

antonioesfandiari wrote etc etc - I stand corrected but - I am sure any one playing fast chess does not look at the face

Bullet is combination of time management and intuition

What you need to do is math for the average rating for both of your ratings. 1370 + 1470 + 1570= 4410 then divide by three equals 1470 which is pretty lucky of you. But this doesn't answer you question but I think it's partial.

I'm thinking that you take 1470 is your average and my answer is blitz rating due to average rating (which is pretty sad that you don't take the high rating of all types of chess).

But that's ultimatum, we can't choose for you. You must choose your rating yourself. It's the only way to prevent conflict of choosing for others.

The rating system in this site is quite bogus. My real FIDE rating=0, 

my blitz/bullet rating=2000

If you want real rating=Blitz rating-2000

Best thing for online ratings is to ignore them on a day to day basis, your rating can go up or down 100 pts in one day easily (especially in bullet).  Just focus on learning, and improving, the rest will follow.  Also it is healthy to play OTB regularly with real people and real pieces.  It is healthy for your overall mentality and your chess.  For most chess students, they care much less about their online rating than they do about their OTB rating, and their performance against friends/rival chess club members .  Visit your local chess club or chess meetup!  https://www.meetup.com/topics/chess/

Bullet is an another art

It's art of smartness, your awareness and decision taking power