To communicate with the kernel, different UNIX systems use different interfaces - not necessarily procfs. It's not a must-have. While it's become quite common with Linux and FreeBSD indeed, OS X (which is based on BSD) does not implement a procfs.

The equivalents to most proc calls would be found in other tools such as sysctl(8) and the sysctl(3) call. Read the manpages (man 8 sysctl or man 3 sysctl) for some examples. Other things you can do with proc cannot be done easily on OS X. This is just a design choice.

See also:

/proc on Mac OS X
A MacFUSE-Based Process File System for Mac OS X
Note that Bash is just a shell (a command line program) that you can use within a terminal emulator (such as Terminal.app on OS X). The shell does not have anything to do with the underlying file system or system architecture. You could switch to any other shell like Zsh or csh – or even another terminal emulator such as iTerm2 – and still use the procfs.