Having worked weddings in both USA and Ireland/UK, the expectations and customs regarding these are different for each nation, but is always asked by couples. 

In the United States, it is most common for it to be an open bar (or no bar for religious reasons), whereas in Ireland and the UK, a cash bar is more common. 

People always assume we never have an open bar in Ireland due to our nations drinking reputation (or as others prefer to call it - being able to handle our drink haha), which may be a contributing factor?! But mainly the difference comes from the varying timelines.

Americans are usually surprised to know that the actual wedding day in Ireland is a full day, as their day would be up to 7 hours max. Out of the hundreds of weddings I have done in California, a timeline from 4pm - 11pm would be the most common, and that is including the ceremony. 

Whereas in Ireland, the ceremony usually starts around 1pm, and the guests are still dancing to the DJ into the early hours of the morning. 

Options for each bar:

Open Bar: 

• Although open, you can select the drinks to offer your guests, and create beautiful menu’s / bar décor to show the options. 
• You can keep the costs down (and the rowdiness) by offering beer and wine only.
• If the venue is BYOB, then you will save a fortune if you did want to offer spirits and have signature cocktails. 

Cash Bar:

• Offer a welcome drink when guests arrive at the reception venue. 
• Offer signature cocktails, and cover their cost for cocktail hour. 
• Put some money behind the bar to cover everyone’s first drink.
• Cover a glass of champagne / prosecco for the toasts.  
• Cover at least one glass of wine during dinner.

These are a few examples of how to have a open bar - but not an extortionate bill, and when a cash bar makes more sense but you do want to offer some celebratory bubbles and wine with the meal.

I read an article a while back about a Scottish wedding that had an open bar, and the bill for the bar ended up costing more than the whole wedding… !!!