Ensembles of bismuth donor spins in silicon are promising storage elements for microwave quantum memories due to their long coherence times which exceed seconds. Operating an efficient quantum memory requires achieving critical coupling between the spin ensemble and a suitable high-quality factor resonator -- this in turn requires a thorough understanding of the lineshapes for the relevant spin resonance transitions, particularly considering the influence of the resonator itself on line broadening. Here, we present pulsed electron spin resonance measurements of ensembles of bismuth donors in natural silicon, above which niobium superconducting resonators have been patterned. By studying spin transitions across a range of frequencies and fields we identify distinct line broadening mechanisms, and in particular those which can be suppressed by operating at magnetic-field-insensitive `clock transitions. Given the donor concentrations and resonator used here, we measure a cooperativity $Csim 0.2$ and based on our findings we discuss a route to achieve unit cooperativity, as required for a quantum memory.
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