This is an 11-episode anime series that came out in 2006 and is based on a manga of the same name. As described in Wikipedia:
Bartender follows the nightlife of Ryū Sasakura (佐々倉 溜, Sasakura Ryū) (voiced by Takahiro Mizushima in the anime), a bartending prodigy who is said to mix the best cocktails anyone has ever tasted. Upon returning from his studies in France, Ryū works as an assistant for a senior bartender at the bar Lapin. He later opened his own bar, the Eden Hall (イーデンホール, Īden Hōru), which is hidden in a nook of the Ginza district in downtown Tokyo. Rumor holds that potential patrons cannot simply find and enter Eden Hall; rather they must be invited in by the host. Sasakura is known to serve the "Glass of the Gods" (神のグラス, Kami no Gurasu), a way of saying that he knows just the right drink to serve in a particular situation.
The only other regular character is Miwa Kurushima (来島 美和, Kurushima Miwa) (voiced by Ayumi Fujimura in the anime), the granddaughter of the owner of the Hotel Cardinal, Taizo Kurushima (来島 泰三, Kurushima Taizō). She is the office lady of the company and requires him to compete for the job of bartender in the hotel. Ryū is initially rejected by Kamishima (神嶋), the manager of the hotel beverage department. However, upon Miwa insistence, Taizo meets Ryū and becomes fascinated by his abilities, requesting her to insist on Ryū to bring him to work in the hotel.
Over the course of the manga, various other figures, all of whom share unusual troubles and heavy burdens, are invited into Eden Hall and are treated to Sasakura's fine drinks, which, with guidance from the young bartender, lead the customers to reflect upon their lives and decide on a course of action to tackle their problems. (footnotes deleted)
If you are interested, you can watch the entire series on this page, just scroll down. This is an episodic anime series so don't worry about having to watch it in order:
Episode 1 "Bartender"
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Episode 2 "Menu of the Heart"
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Episode 3 "Glass of Regret"
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Episode 4 "Amber Dream"
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Episode 5 "Things Forgotten in a Bar"
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Episode 6 "The Story Inside the Glass"
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Episode 7 "Closed Day for the Bar"
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Episode 8 "The Lie at the Counter"
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Episode 9 "The Bar's Face"
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Episode 10 "Christmas Miracle"