  We propose an implementation of bivariate bicycle codes (Nature {\bf 627},
778 (2024)) based on long-range Rydberg gates between stationary neutral atom
qubits. An optimized layout of data and ancilla qubits reduces the maximum
Euclidean communication distance needed for non-local parity check operators.
An optimized Rydberg gate pulse design enables $\sf CZ$ entangling operations
with fidelity ${\mathcal F}>0.999$ at a distance greater than $12~\mu\rm m$.
The combination of optimized layout and gate design leads to a quantum error
correction cycle time of $\sim 1.2~\rm ms$ for a $[[144,12,12]]$ code, an order
of magnitude improvement over previous designs.
