Thermonuclear bursts from slowly accreting neutron stars ( NSs ) have proven difficult to detect , yet they are potential probes of the thermal properties of the neutron star interior . During the first year of a systematic all-sky search for X-ray bursts using the Gamma-ray Burst Monitor ( GBM ) aboard the Fermi Gamma-ray Space Telescope we have detected 15 thermonuclear bursts from the NS low-mass X-ray binary 4U 0614+09 , when it was accreting at nearly 1 % of the Eddington limit . We measured an average burst recurrence time of 12 \pm 3 d ( 68 % confidence interval ) between March 2010 and March 2011 , classified all bursts as normal duration bursts and placed a lower limit on the recurrence time of long/intermediate bursts of 62 d ( 95 % confidence level ) . We discuss how observations of thermonuclear bursts in the hard X-ray band compare to pointed soft X-ray observations , and quantify such bandpass effects on measurements of burst radiated energy and duration . We put our results for 4U 0614+09 in the context of other bursters and briefly discuss the constraints on ignition models . Interestingly , we find that the burst energies in 4U 0614+09 are on average between those of normal duration bursts and those measured in long/intermediate bursts . Such a continuous distribution in burst energy provides a new observational link between normal and long/intermediate bursts . We suggest that the apparent bimodal distribution that defined normal and long/intermediate duration bursts during the last decade could be due to an observational bias towards detecting only the longest and most energetic bursts from slowly accreting NSs .