Question

Is our sun rotating around a bigger star?

Answer 1

No, but...

Explanation:

Our sun orbits around the centre of mass of our galaxy. It has no large enough nearby companion star.

While we are on this topic, it may be interesting to note that the Earth does not exactly orbit the Sun nor the Sun the Earth, but they both orbit their barycentre (centre of mass). To a good approximation this boils down to the Earth orbiting the sun since the Sun is much more massive than the Earth and the barycentre is well inside the Sun, but the Earth will cause a very slight "wobble" in the position of the Sun as it orbits.

On the other hand, Jupiter is massive enough and close enough to the Sun that their barycentre is outside the Sun, but only by about `7`%. So as Jupiter "orbits the Sun", the Sun actually traces out a roughly circular ellipse larger than its radius, around their barycentre.