Explicit models of families of genus 2 curves with multiplication by √D are known for D= 2, 3, 5. We obtain generic models for genus 2 curves over ℚ with real multiplication in 12 new cases, including all fundamental discriminants D < 40. A key step in our proof is to develop an algorithm for minimisation of conic bundles fibred over ℙ2. We apply this algorithm to simplify the equations for the Mestre conic associated to the generic point on the Hilbert modular surface of fundamental discriminant D < 100 computed by Elkies-Kumar.