Black Hole Mass Scaling Relations for Spiral Galaxies. I. $M_{\rm
  BH}$-$M_{\rm *,sph}$
  The (supermassive black hole mass, $M_\text{BH}$)-(bulge stellar mass,
$M_{\rm*,sph}$) relation is, obviously, derived using two quantities. We
endeavor to provide accurate values for the latter via detailed multicomponent
galaxy decompositions for the current full sample of 43 spiral galaxies having
directly measured $M_\text{BH}$ values; 35 of these galaxies have been alleged
to contain pseudobulges, 21 have water maser measurements, and three appear
bulgeless. This more than doubles the previous sample size of spiral galaxies
with a finessed image analysis. We have analyzed near-infrared images,
accounting for not only the bulge, disk (exponential, truncated, or inclined),
and bar but also for spiral arms and rings and additional central components
(active galactic nuclei (AGNs), etc.). A symmetric Bayesian analysis finds
$\log\left(M_\text{BH}/M_{\odot}\right)=\left(2.44_{-0.31}^{+0.35}\right)\log\left\{M_{\rm*,sph}/[\upsilon(1.15\times10^{10}\,M_{\odot})]\right\}+(7.24\pm0.12)$,
with $\upsilon$ a stellar mass-to-light ratio term. The level of scatter equals
that about the $M_{\rm BH}$-$\sigma_*$ relation. The nonlinear slope rules out
the idea that many mergers, coupled with the central limit theorem, produced
this scaling relation, and it corroborates previous observational studies and
simulations, which have reported a near-quadratic slope at the low-mass end of
the $M_\text{BH}$-$M_{\rm*,sph}$ diagram. Furthermore, bulges with AGNs follow
this relation; they are not offset by an order of magnitude, and models that
have invoked AGN feedback to establish a linear $M_{\rm BH}$-$M_{\rm*,sph}$
relation need revisiting. We additionally present an updated
$M_\text{BH}$-(S\'ersic index, $n_\text{sph}$) relation for spiral galaxy
bulges with a comparable level of scatter and a new $M_{\rm*,sph}$-(spiral-arm
pitch angle, $\phi$) relation.
