Thanks to Aditya Kumar; acceptable solution:
gdb -batch -ex "run" -ex "bt" ${my_program} 2>&1 | grep -v ^"No stack."$
If the program needs arguments:
gdb -batch -ex "run" -ex "bt" --args ${my_program} param1 param2 \
param3 ... 2>&1 | grep -v ^"No stack."$