Testosterone is a steroid, which is a lipid. Lipids are hydrophobic; they don’t mix well with water.
Testosterone is a hormone. All hormones, by definition, must travel in th blood plasma to get from the glands that secrete them to the target organs they’re meant to stimulate.
Blood plasma is 92% water.
See the problem here?
Hydrophobic hormones travel in the blood by binding to a hydrophilic carrier protein. This is one of the functions of blood albumin and the function of some of the alpha and beta globulins in the blood plasma. All the steroid hormones as well as thyroid hormone require carriers.
A hormone attached to a carrier is called bound hormone —bound tetosterone, for example. Carrier proteins, however, can’t cross cell membranes to escort the hormone through the capillary walls into the target tissue. To pass out of the bloodstream and get to the cells that need it, testosterone and other such proteins must (in a manner of speaking) detach from their carrier and hurry up and pass through the cell membranes to get through the capillary wall and into the target cells. For that brief moment, the hormone is called unbound (free, bioavailable) hormone. It’s a very small fraction of the total level of that hormone in the blood, but only this free hormone is able to have any effect on the target cells.
There’s a dynamic equilibrium between the bound and unbound hormone fractions. I don’t offhand know exact numbers and I think it varies from one hormone and carrier to another, but I believe a reasonable ballpark number is that an average hydrophobic protein in the blood is 98–99% bound and 1–2% unbound. As unbound hormone is taken up by target tissues, the equilibrium is shifted and more hormone dissociates from its carrier and becomes available for uptake.
Here’s a figure that a web site plagiarized from one of my books. Yellow represents hydrophilic hormones that mix freely with blood plasma and tissue fluid. Blue represents hydrophobic hormones that require a carrier. Only the unbound molecules of the latter can cross from bloodstream to target cell.
One source I just looked up seems to have been written by a math-impaired writer in the Cleveland Heart Lab. It says of all the testosterone in the blood, 60% is bound to sex hormone–binding globulin (SHBG), 50% is bound to albumin, and 1–2% is free and bioavailable. Go figure.