Is there any professional way to decline team-building activities
without burning bridges or is it just one of those times where you
have to suck it up ?
The activity: everyone is invited for dinner to a restaurant near our
office and then they are going to mini-putt. It's going to cost at the
very least 30$ at the restaurant and 15$ for the mini-putt out of my
pockets. This is actually another reason I don't want to go.
Unfortunately, declining team-building activities is often awkward, even when they are optional.
Your company holds these events because they want to form stronger teams. Opting out can sometimes unintentionally (or intentionally) signal that you aren't willing to help build a stronger team.
But in this particular case, since it's a Friday and dinner is involved, you have a very reasonable way out. Just say something along the lines of "Oh, I'm sorry, but I'll have to decline. I have other dinner reservations for that Friday."
You might also consider your role in the company as a factor before you make your decision. If you are part of management, you may be expected to show leadership by attending. If you are not part of management, your absence may stick out less.
I was recently trying to politely bow out of a company-sponsored (free) activity. My boss privately told me "as part of management, you are expected to be there". So I rearranged my plans and went to the event.
As an aside, I think it's rather odd that a company team-building activity requires you to pay for the dinner and the activity out of your own pocket. To me that signals that the company might think it's somewhat important to build the team, but isn't willing to put it's own money toward doing so - thus it's not really that important. Due to that fact, I suspect you will get less of a negative response to your declining the invitation, than if the event had been at company expense.
It also gives you the possibility of responding with something like "Sorry, I'm trying to save money and would rather not spend the $45 on this activity." It would be hard to argue with that as a response. (But as David K correctly points out - there is a potential downside to this response. The company could choose to cover the cost - then you might be expected to attend.)