We observe trilobite-like states of ultracold 85Rb2 molecules, in which a ground-state atom is bound by the electronic wavefunction of its Rydberg-atom partner. We populate these states through the ultraviolet excitation of weakly-bound molecules, and access a regime of trilobite-like 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, trilobite-like 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.