  Dirac fermions display a singular response against magnetic and electric
fields. A distinct manifestation is large diamagnetism originating in the
interband effect of Bloch bands, as observed in bismuth alloys. Through
$^{209}$Bi NMR spectroscopy, we extract diamagnetic orbital susceptibility
inherent to Dirac fermions in the semiconducting bismuth alloys
Bi$_{1-x}$Sb$_x$ ($x = 0.08 - 0.16$). The $^{209}$Bi hyperfine coupling
constant provides an estimate of the effective orbital radius. In addition to
the interband diamagnetism, Knight shift includes an anomalous
temperature-independent term originating in the enhanced intraband diamagnetism
under strong spin-orbit coupling. The nuclear spin-lattice relaxation rate
$1/T_1$ is dominated by orbital excitation and follows cubic temperature
dependence in the extensive temperature range. The result demonstrates the
robust diamagnetism and low-lying orbital excitation against the small gap
opening, whereas $x$-dependent spin excitation appears at low temperatures.
