>>48934987People say 14, but Bianca is handing you Poké Balls with starters two years later. She also appears to be a young adult. Cheren is not just a gym leader, but also a teacher of a children’s school.
I’d say they are at least 16 or morally equivalent to our world’s 16 in BW. GF says 14 because they didn’t have enough confidence to make an older protagonist cannon. At this point, they really should allow you to play with an age range up to at least 18 due to the wider reach of the franchise (I’d say higher, but they would likely resist due to how it affects the Mom mechanic in every story).