The brace should be installed with the 2in dimension vertical, otherwise you will get a lot more flexing in the brace. You may find you need e.g., 3in depth.
If you glue two pieces of the 2in x 3/4in in a "T" arrangement, this would be even stronger and more rigid.
To install drill a horizontal hole through from one end through to the other. Diameter should match the size of the bolt. I would use at least 5/16in, perhaps 3/8in.
Drill a larger hole with a Forstner bit to accommodate a washer/nut or washer/head of the bolt. The Forstner will provide a flat bottom for the washers.
If you use a lock nut (nut with plastic collar insert), this should not come apart during use.