> The first rigorous and accurate scientific measurement of the Earth-Sun distance was made by Cassini in 1672 by parallax measurements of Mars. He and another astronomer observed Mars from two places simultaneously. A century later, a series of observations of transits of Venus provided an even better estimate.

http://curious.astro.cornell.edu/about-us/41-our-solar-syste...

We can't bounce signals off the sun, but we can do "interplanetary radar" bouncing signals off at least the nearby planets.

Knowing those distances, the distance to the sun becomes a trigonometry problem.

The video of Terence Tao I linked addresses that and many other questions about climbing the cosmic distance ladder.