Elementwise mapping preserving static type

I would like to map a vector of vectors (the latter static) elementwise, so that the static type is preserved.

# setup
using StaticArrays, Test
bs = [SVector{4}(randn(4)...) for _ in 1:9] # 9 is "large" in real life
A = randn(9, 9)

# one solution
function f(A, bs)
    X = A \ mapreduce(permutedims, vcat, bs)

xs = @inferred f(A, bs) # OK
typeof(xs)              # SArray{Tuple{4},Array{Float64,1},1,4}

I have solved my immediate problem (a hot loop using these arrays experienced a 30x speedup, yay!), but I am curious if there is an idiomatic solution, one that ideally propagates the static shape information to xs when applicable (and also works when bs contains plain vanilla Vectors).