Ok. Yes, it looks like I spoke too soon and I have the same output in your screenshot. Sorry! Looks like another user offered a solution. You could also pipe to a dollar sign which is probably not ideal:
Orange %>%
group_by(Tree) %>%
nest() %>%
mutate(m1_bam = map(data, ~ bam(formula = circumference ~ 1 + age, family = gaussian, data = .x)),
m1_smry = map(m1_bam, ~ tidy(.x))
m1_beta = map(m1_smry, ~ .x$p.table)
) %>%
.$m1_smry
It looks like folks are working on ways to tidy() the output from a bam model