The ornamental design for racing bicycle handlebars, as shown and described.
FIG. 1 is a front perspective view of the racing bicycle handlebars in accordance with the present invention;
FIG. 2 is a front elevational view thereof;
FIG. 3; is a left side elevational view thereof, the right side being a mirror image thereof; and,
FIG. 4 is a top plan view thereof, the bottom being unadorned.
The broken lines illustrate portions of the racing bicycle handlebars that form no part of the claimed design. The broken lines showing crosshair symbols in FIGS. 3-4 form no part of the claimed design.