We observe "trilobitelike" states of ultracold (85)Rb(2) molecules, in which a ground-state atom is bound by the electronic wave function of its Rydberg-atom partner. We populate these states through the ultraviolet excitation of weakly bound molecules, and access a regime of trilobitelike states at low principal quantum numbers and with vibrational turning points around 35 Bohr radii. This demonstrates that, unlike previous studies that used free-to-bound transitions, trilobitelike states can also be excited through bound-to-bound transitions. This approach provides high excitation probabilities without requiring high-density samples, and affords the ability to control the excitation radius by selection of the initial-state vibrational level.