Sex isn't the only way to deepen a relationship, but it is probably the surest.
Without that, there are walls of fear to be overcome.
Dating a younger man can be highly satisfying for various reasons, not the least being a sense of youthful adventure and freedom that such a partner can bring into the life of a mature woman.
At the same time there are certain things you better avoid if you wish to have the best of a younger guy minus the complexities of age disparity.
Instead of apologizing for being shy, embrace it, work with it, and be yourself.