Production of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>b</mml:mi><mml:mover accent="true"><mml:mi>b</mml:mi><mml:mo stretchy="false">¯</mml:mo></mml:mover></mml:math> at forward rapidity in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>p</mml:mi><mml:mo>+</mml:mo><mml:mi>p</mml:mi></mml:math> collisions at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msqrt><mml:mi>s</mml:mi></mml:msqrt><mml:mo>=</mml:mo><mml:mn>510</mml:mn><mml:mtext> </mml:mtext><mml:mtext> </mml:mtext><mml:mi>GeV</mml:mi></mml:math>

The cross section of bottom quark-antiquark ($b\overline{b}$) production in $p+p$ collisions at $\sqrt{s}=510\text{ }\text{ }\mathrm{GeV}$ is measured with the PHENIX detector at the Relativistic Heavy Ion Collider. The results are based on the yield of high mass, like-sign muon pairs measured within the PHENIX muon arm acceptance ($1.2&lt;|y|&lt;2.2$). The $b\overline{b}$ signal is extracted from like-sign dimuons by utilizing the unique properties of neutral $B$ meson oscillation. We report a differential cross section of $d{\ensuremath{\sigma}}_{b\overline{b}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\mu}}^{\ifmmode\pm\else\textpm\fi{}}}/dy=0.16\ifmmode\pm\else\textpm\fi{}0.01\text{ }(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.02\text{ }(\mathrm{syst})\ifmmode\pm\else\textpm\fi{}0.02\text{ }(\text{global})\text{ }\text{ }\mathrm{nb}$ for like-sign muons in the rapidity and ${p}_{T}$ ranges $1.2&lt;|y|&lt;2.2$ and ${p}_{T}&gt;1\text{ }\text{ }\mathrm{GeV}/c$, and dimuon mass of $5--10\text{ }\text{ }\mathrm{GeV}/{c}^{2}$. The extrapolated total cross section at this energy for $b\overline{b}$ production is $13.1\ifmmode\pm\else\textpm\fi{}0.6\text{ }(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}1.5\text{ }(\mathrm{syst})\ifmmode\pm\else\textpm\fi{}2.7\text{ }(\text{global})\text{ }\ensuremath{\mu}\mathrm{b}$. The total cross section is compared to a perturbative quantum chromodynamics calculation and is consistent within uncertainties. The azimuthal opening angle between muon pairs from $b\overline{b}$ decays and their ${p}_{T}$ distributions are compared to distributions generated using ps pythia6, which includes next-to-leading order processes. The azimuthal correlations and pair ${p}_{T}$ distribution are not very well described by pythia calculations, but are still consistent within uncertainties. Flavor creation and flavor excitation subprocesses are favored over gluon splitting.