FRB 20240114A is a hyperactive repeating fast radio burst (FRB) source discovered by the CHIME/FRB Collaboration in January 2024. The source has been followed up by numerous radio telescopes, including MeerKAT, uGMRT, and FAST, and has been localized to a dwarf star-forming galaxy at a redshift of z~0.13 with a confirmed persistent radio source. We report observations of FRB 20240114A with the Effelsberg 100-m radio telescope using the Ultra BroadBand (UBB) receiver, covering 1.3-6.0GHz. Over four epochs, we detected more than 700 bursts, providing an unprecedented broadband dataset for statistical analysis of this active repeater. We performed a comprehensive study of the bursts' morphologies, occurrence rates, spectral and temporal widths, and waiting-time distributions across six sub-bands spanning the UBB frequency range. The bursts exhibit four main spectral morphologies, including simple, complex, and frequency-drifting structures. No bursts were detected across the full 1.3-6GHz band, confirming band-limited emission. Burst widths show modest frequency evolution, while fractional bandwidths remain roughly constant at ~10%. Burst rates vary strongly with time and frequency, partly influenced by scintillation. The waiting-time distribution is bimodal, with largely independent bursts and short-timescale clustering on ~10ms, indicating a characteristic emission timescale. The source can switch emission frequencies by GHz on seconds and by ~700MHz on millisecond timescales, implying a highly agile emission mechanism.