In [11]: s = pd.Series(['aa', 'ab', 'ca', np.nan])

In [12]: s.str.startswith('a', na=False)
Out[12]:
0     True
1     True
2    False
3    False
dtype: bool

In [13]: s.str.contains('^a', na=False)
Out[13]:
0     True
1     True
2    False
3    False
dtype: bool

In [14]: s.str.startswith('a')  # can't use as boolean mask
Out[14]:
0     True
1     True
2    False
3      NaN
dtype: object

s.str.contains('a', case = False)