Is there bacteria growth in butter?

Bacteria can grow in butter, but the very high fat content means it is not ideal for bacterial growth the way, say, milk is. Butter is made from milk so as long as the milk is pasteurised first (and it always is) your butter is pretty safe.

Refrigerated butter wont grow bacteria unless it already contains psychotrophs. Psychotrophs are bacteria that especially grow at cool temperatures. An example of this is the bacteria Pseudomonas. Psychotrophs are tested for, and the butter must be cleared before it can be sold.

Other bacteria such as coliforms (eg E.coli) can grow in butter that is kept at room temperature, but this is usually a result of contamination from the manufacturing process. Butter that contain coliforms can not be sold according to industry standards. If you don't refrigerate your butter and don't keep good hygiene you could potentially contaminate your own butter at home.

It is not likely though because as I mentioned at the start, the high fat content doesn't allow for a lot of growth.

All dairy has a LOT of bacteria in it. Bacteria like streptococcus (yes, like strep throat) are what make dairy so good. They produce some of the characteristic esters and other compounds in dairy foods like butter. In fact, the 'buttery' taste characteristic of chardonnay is the result of the winemaker inoculating the wine with bacteria that converts the tart malic acid into smooth and buttery lactic acid.

According to the website below, Streptococcus diacetilactis is the prominent bacterium in butter.

Don't worry, these are not virulent strains and will not hurt you. If you freeze the butter the bacteria in it will obviously not be growing and is not a bad idea if your not planning on using the butter anytime soon. But for the most part butter will keep just fine and the natural bacteria in it won't spoil it, just keep it covered to keep out foreign bacteria and fungus.