Write a Python function `match_a_followed_by_b` that takes a string as input and returns `True` if the string contains an 'a' followed by one or more 'b's, and `False` otherwise. Use regular expressions to solve this problem.
#### Example Usage
```python [main.nopy]
print(match_a_followed_by_b("ab")) # Output: True
print(match_a_followed_by_b("a")) # Output: False
print(match_a_followed_by_b("abb")) # Output: True
print(match_a_followed_by_b("b")) # Output: False
```
#### Constraints
- The function should be case-sensitive.
- The input string can be of any length, including empty.