Bleach TYBW has only recently revealed the original identity of Retsu Unohana to be Yachiru Unohana. She was the first Kenpachi and is currently tasked with teaching Zaraki Kenpachi, her sword fighting technique called Zanjitsu.
While the Squad 11 captain already lacked fighting techniques, he was also the only captain to have not acquired a Bankai, which is strange given his strength level.
With Zaraki Kenpachi finally getting the opportunity to learn Zanjitsu from the person he admires the most, chances are that he could acquire his Bankai.
But what is the usual way for Gotei 13 captains to learn Bankai? It was certainly different for Kisuke Urahara and Ichigo Kurosaki, with both of them shortening their training time using Tenshintai. So, what is the norm?
A Shinigami would typically take about 10 years to master their Bankai in Bleach
According to what Yoruichi revealed to Ichigo during his Bankai training, a Shinigami usually takes about ten years to train and fully master Bankai. She explained how the essence of Shikai was to communicate and synchronize with one's Zanpakuto spirit. Meanwhile, Bankai required a Shinigami to externalize the Zanpakuto spirit and force them into submission.
This process requires a Shinigami to be able to summon their Zanpakuto spirit into the real world, but this move usually takes an individual about ten years of training to perform.
This would exclude the battle experience the Shinigami would go through during the ten years. Thus, a Bankai is generally a state that only a small number of Shinigami have attained over the history of the Soul Society.
This is why Byakuya Kuchiki was shocked upon witnessing Ichigo perform Bankai with only three days of training. As for the ten-year training period, a Shinigami must master the inherent abilities of the sealed form Zanpakuto.
Then, they must master the Shikai form and establish a strong connection, through which they will be able to draw out the power of the Zanpakuto’s soul.
Do the Gotei 13 captains need to be able to perform Bankai to become captains?
No, there is no requirement for Gotei 13 captains to be able to perform Bankai to become captains. Being able to perform Bankai is just an indication of a Shinigami's strength and perseverance to attain the true powers of their Zanpakuto, however, nowhere has it been stated that a Shinigami needs to be able to perform Bankai to become captain.
A major example of the same is Zaraki Kenpachi, the captain of Squad 11 of the Gotei 13. He had no connection with his Zanpakuto and was also unaware of its name until his fight against squad 4 captain and the first Kenpachi, Yachiru Unohana, ended during the Thousand-Year Blood War arc.
In fact, Zaraki Kenpachi became the captain of Squad 11 by the other method other than recommendations, that is, through combat. He acquired the captain's Haori after he defeated the previous captain of squad 11 in a death battle in which he came out victorious.