C, 273 bytes

main(_,a){_=fopen("w.c","w");fputs("main(){char a[30000],*p=a;",_);x:a=getchar();fputs(a-62?a-60?a-43?a-45?a-46?a-44?a-91?a-93?a+1?"":"}":"}":"while(*p){":"*p=getchar();":"putchar(*p);":"--*p;":"++*p;":"--p;":"++p;",_);if(a!=-1)goto x;fclose(_);system("cc w.c;./a.out");};

Takes input from stdin.

This relies a little bit on the environment, but is pretty consistent. This is effectively the eval solution for c. It writes an appropriate C program to the file w.c, compiles it, and runs it as the desired executable. Thus as a bonus effect this actually compiles the bf code and leaves a.out as a binary for it. Note that depending on the system you may need to modify the last string. In particular most windows c compilers call the default executable "a.exe". Luckily as far as I can tell, they all have the same length so the bytecount is the same. (though if you don't have a cc defined you may need to add a letter such as gcc to the compile command, adding 1 byte).

I am aware that this thread is a bit old, but I didn't see this style of C solution yet, so I thought I'd add it.

C (gcc), 273 268 bytes

main(_,a){_=fopen("w.c","w");fputs("main(){char a[30000],*p=a;",_);x:a=getchar();fputs(a-62?a-60?a-43?a-45?a-46?a-44?a-91?a-93?~a?"":"}":"}":"while(*p){":"*p=getchar();":"putchar(*p);":"--*p;":"++*p;":"--p;":"++p;",_);if(~a)goto x;fclose(_);system("cc w.c;./a.out");};

Try it online!

-5 thanks to ceilingcat

Takes input from stdin.

This relies a little bit on the environment, but is pretty consistent. This is effectively the eval solution for c. It writes an appropriate C program to the file w.c, compiles it, and runs it as the desired executable. Thus as a bonus effect this actually compiles the bf code and leaves a.out as a binary for it. Note that depending on the system you may need to modify the last string. In particular most windows c compilers call the default executable "a.exe". Luckily as far as I can tell, they all have the same length so the bytecount is the same. (though if you don't have a cc defined you may need to add a letter such as gcc to the compile command, adding 1 byte).

I am aware that this thread is a bit old, but I didn't see this style of C solution yet, so I thought I'd add it.