Can I be arrested for drinking at a bar and then walking home?
In short, yes, if you are intoxicated at a level where you may pose a danger to yourself or others around you. The determination on whether you are so intoxicated or drunk in public that you pose a danger to yourself or others is left initially to the arresting officer.
The arresting officer will observe your demeanor, speech, gait, and whether you stumble or repeatedly fall down. Other aspects, such as blood shot eyes, smell of alcohol, and slurred speech also play a role in an officer's decision on whether to make an arrest for Public Intoxication, as do factors such as stumbling or walking into traffic, shouting or yelling, and rowdy behavior.
Because a bar is a public place, you could be arrested there, however, it's far more likely that the bar would kick a person out first, and then call the police. This is especially true if the person is hostile or staring arguments and fights within the bar.