One approach is to replace the function in Foo before Bar is compiled.

# Compile foo
use Foo;

# Replace (mock) a function in Foo
BEGIN {
    no warnings 'redefine';
    *Foo::get_db_value = sub { return 2 }
}

# Compilation of Bar finds mocked function, not original function
# (Foo was already loaded so is not recompiled)
use Bar;

# Test function
is(Bar::bar_func(), 84, "bar_func works as advertised");
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You could replace the "2" with a package variable (or package-scoped lexical) if you want to be able to change the value returned for use in different tests.