Her money didn't get him to Washington. She "made" her money in owning radio stations after he was in. I don't remember the details, but his connections somehow got her favorable treatment. There's a biography called "LBJ - Means of Ascent" (I think) that covers it pretty well....
She bought an AM radio station in the high end of the AM spectrum (e.g. 1450), which doesn't reach out very far and so was cheap. He got legislation passed that switch the frequency down to the other end of the spectrum(e.g. 710) which gave a range almost from Texas to Canada - a huge difference in value, and what they could charge for ads.
Ladybird had money from her family but she and LBJ made big money together. She bought the land on Clear Lake just in time to sell it to NASA. I remember when that happened. I have read Means of Assent and Master of the Senate, biographies of LBJ, and by the way, LBJ DID kill Kennedy. There is absolutely no doubt in my mind. The more you know about LBJ the clearer that becomes to you. Absolutely ruthless and he HAD to be president.