How do I loop through only directories in bash?

You can specify a slash at the end to match only directories:

for d in */ ; do
    echo "$d"
done

You can test with -d:

for f in *; do
    if [ -d "$f" ]; then
        # $f is a directory
    fi
done

This is one of the file test operators.

Beware that choroba's solution, though elegant, can elicit unexpected behavior if no directories are available within the current directory. In this state, rather than skipping the for loop, bash will run the loop exactly once where d is equal to */:

#!/usr/bin/env bash

for d in */; do
    # Will print */ if no directories are available
    echo "$d"
done

I recommend using the following to protect against this case:

#!/usr/bin/env bash

for f in *; do
    if [ -d "$f" ]; then
        # Will not run if no directories are available
        echo "$f"
    fi
done

This code will loop through all files in the current directory, check if f is a directory, then echo f if the condition returns true. If f is equal to */, echo "$f" will not execute.