  We determine the normalisation of scalar and pseudoscalar current operators
made from non-relativistic $b$ quarks and Highly Improved Staggered light
quarks in lattice Quantum Chromodynamics (QCD) through $\mathcal{O}(\alpha_s)$
and $\Lambda_{\text{QCD}}/m_b$. We use matrix elements of these operators to
extract $B$ meson decay constants and form factors, then compare to those
obtained using the standard vector and axial-vector operators. This provides a
test of systematic errors in the lattice QCD determination of the $B$ meson
decay constants and form factors. We provide a new value for the $B$ and $B_s$
meson decay constants from lattice QCD calculations on ensembles that include
$u$, $d$, $s$ and $c$ quarks in the sea and those which have the $u/d$ quark
mass going down to its physical value. Our results are $f_B=0.196(6)$ GeV,
$f_{B_s}=0.236(7)$ GeV and $f_{B_s}/f_B =1.207(7)$, agreeing well with earlier
results using the temporal axial current. By combining with these previous
results, we provide updated values of $f_B=0.190(4)$ GeV, $f_{B_s}=0.229(5)$
GeV and $f_{B_s}/f_B = 1.206(5)$.
