Summary
The 'Create Detailed Border' option is unavailable/grayed out.
Procedure
Business Analyst Server uses Street Map as the Network Analyst Solver, which is the default setting.
The 'Create Detailed Border' option is supported if 'Network Service' is set as the 'Network Analyst Solver'.
Change the 'Network Analyst Solver' setting to 'Network Service' to use the 'Create Detailed Border' option in the drive time polygons.