This one has come up a number of times before and, unfortunately, Tableau does not like to do tables with no measures (which is how I am interpreting your case). And so, you will only get scroll bars in a table when you have measures. But even that won't do it for you because even if you did have a measure the scroll bar would only apply to the measures and not the entire table. This also applies to Tooltips which only show up when you mouse over a measure. You cannot get a customizable toolip over any of the headers in a table -- just measures.
I have dashboards with a graphic above and details table below. I have no practical use for a measure in the details table as users interact with the graphic to dynamically filter the details table. I would love to have: a) a scroll bar for the entire table; b) a customizable tooltip for the headers in the details table. As it is right now, I squeeze what I can into the table and then use a Tableau "trick" to give me a tooltip over the last column.
I know this doesn't help much but at least you knnow you aren't alone!
I don't get why the designers of Tableau stubbornly force users to find workarounds for simple tasks!?
It's quite obvious from the way people use data and tables that a horizontal scroll bar would be more useful than simply hiding the columns in a way that they cant be accessed. It seems crazy!?