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Understanding the Sun’s role in past climate change requires knowledge of solar variability over millennia. While direct sunspot records span only the last 400 years, longer-term changes are inferred from cosmogenic radionuclides like 14C and 10Be in tree rings and ice cores. Their production reflects variations in galactic cosmic ray flux, modulated by Earth’s and Sun’s magnetic fields - the latter is tied to solar activity. We present a Bayesian model that jointly reconstructs solar modulation and the global geomagnetic field over the Holocene. Extending previous work, our model directly incorporates 14C and 10Be production rate data and thermoremanent magnetic records. A flexible prior allows for bimodality and explicit long-term trends in solar activity. The reconstruction shows a clear separation of grand solar minima and a normal mode. Additionally, we explore the recovery of an 11-year cycle in solar modulation.