As much as i love Yamato, even i don't think that she will reach 1 billion on her first bounty. Her best feat to date is holding off Kaido on the roof top, but the problem is i don't think CP0 saw that (we never saw one of the mary's observing their fight like Zoro vs King for example) <which has me believe that her feats against kaido might not be counted for her first bounty.
Knowing Oda, my safest bet would be 550 million, the same as Ace's bounty. 550 million would also make Yamato higher than Ulti's bounty (400 million) who was shown weaker than Yamato, and also higher than who's who's bounty (546 million), the strongest Tobi Roppo.
I think its more likely that Yamato will reach the 1 billion range on her second bounty.
Knowing Oda, my safest bet would be 550 million, the same as Ace's bounty. 550 million would also make Yamato higher than Ulti's bounty (400 million) who was shown weaker than Yamato, and also higher than who's who's bounty (546 million), the strongest Tobi Roppo.
I think its more likely that Yamato will reach the 1 billion range on her second bounty.