The BSS is a placeholder defined in your executable (or ELF) format. So it does not take up disk space, but only specifies what memory region should be allocated by the linker or loader.
The exact operation depends on the operating system. Since you refer to ELF, I assume it is for use in an embedded system. If you build for ROMmable code, your linker cmd file will map the BSS to a static address region.
In case you build for an operating system (i.e. Linux), the loader from the operating system will perform a relocation pass, in which it maps all locations marked as relative in the excecutable format to physical or logical locations in memory.
Because you mention always seeing the same value, this indicates that the process is repeatable for your system. Expect to see changes when you change linker files (i.e. address regions), link order (i.e. modules will get assigned space in a different order) or operating system.
Wether or not you use the BSS values, the address will remain the same for the process you run.