Short answer
Most wedding should plan for 2 or 3 bartenders for the night.
The reason
The goal of the night is to keep a smooth running bar, we don't want people waiting in line for 20 minutes just to get 3 shots for the friends or family on the dance floor. While most bartenders might suggest 1 bartender per 75 people with the right cocktails and behind the bar set up you can easily do 1 bartender per 100 people.
Why do I say 1 per 100. Well the speed of a bar isn't just the speed of a bartender it also depends on:
How complicated the cocktails are
Whether guests are ordering the shots
How many bars are set up
A wedding with 150 guests and three signature cocktails is going to move very differently than a wedding with 300 guests ordering tequila shots all night.
In practice
Let's say you have 150 guests for your wedding.
2 bartenders usually will keep everything running smooth between cocktail and dinner hours. Once the dance floor opens though? That's when things get fun. Guests start ordering rounds, people try the signature drinks, and suddenly the bar gets busy again.
This is why wedding with 250 or even 300 may want 3 bartenders while events with over 300 will want 3 or 4 bartenders plus and extra bar set either on the dance floor or on the opposite side of the other bar. Remember speedy service keeps your gets on the dance floor and your party looking like a good time.
Bartender Guide by Guest Count
Example:
50–100 guests → 1 bartender
100–200 guests → 2 bartenders
200–300 guests → 3 bartenders
300+ guests → 3–4 bartenders + second bar