diff --git a/doc/source/whatsnew/v1.4.0.rst b/doc/source/whatsnew/v1.4.0.rst
index 8b51fe2db7641..b83fd0504342c 100644
--- a/doc/source/whatsnew/v1.4.0.rst
+++ b/doc/source/whatsnew/v1.4.0.rst
@@ -544,6 +544,8 @@ Datetimelike
 - Bug in in calling ``np.isnan``, ``np.isfinite``, or ``np.isinf`` on a timezone-aware :class:`DatetimeIndex` incorrectly raising ``TypeError`` (:issue:`43917`)
 - Bug in constructing a :class:`Series` from datetime-like strings with mixed timezones incorrectly partially-inferring datetime values (:issue:`40111`)
 - Bug in addition with a :class:`Tick` object and a ``np.timedelta64`` object incorrectly raising instead of returning :class:`Timedelta` (:issue:`44474`)
+- Bug in adding a ``np.timedelta64`` object to a :class:`BusinessDay` or :class:`CustomBusinessDay` object incorrectly raising (:issue:`44532`)
+-
 
 Timedelta
 ^^^^^^^^^
diff --git a/pandas/_libs/tslibs/offsets.pyx b/pandas/_libs/tslibs/offsets.pyx
index f689b8ce242e5..968a4d0198f09 100644
--- a/pandas/_libs/tslibs/offsets.pyx
+++ b/pandas/_libs/tslibs/offsets.pyx
@@ -353,6 +353,9 @@ cdef class BaseOffset:
     """
     Base class for DateOffset methods that are not overridden by subclasses.
     """
+    # ensure that reversed-ops with numpy scalars return NotImplemented
+    __array_priority__ = 1000
+
     _day_opt = None
     _attributes = tuple(["n", "normalize"])
     _use_relativedelta = False
@@ -434,6 +437,10 @@ cdef class BaseOffset:
         if not isinstance(self, BaseOffset):
             # cython semantics; this is __radd__
             return other.__add__(self)
+
+        elif util.is_array(other) and other.dtype == object:
+            return np.array([self + x for x in other])
+
         try:
             return self.apply(other)
         except ApplyTypeError:
@@ -448,7 +455,8 @@ cdef class BaseOffset:
         elif not isinstance(self, BaseOffset):
             # cython semantics, this is __rsub__
             return (-other).__add__(self)
-        else:  # pragma: no cover
+        else:
+            # e.g. PeriodIndex
             return NotImplemented
 
     def __call__(self, other):
@@ -767,8 +775,6 @@ cdef class SingleConstructorOffset(BaseOffset):
 # Tick Offsets
 
 cdef class Tick(SingleConstructorOffset):
-    # ensure that reversed-ops with numpy scalars return NotImplemented
-    __array_priority__ = 1000
     _adjust_dst = False
     _prefix = "undefined"
     _attributes = tuple(["n", "normalize"])
diff --git a/pandas/tests/tseries/offsets/test_business_day.py b/pandas/tests/tseries/offsets/test_business_day.py
index 92176515b6b6f..c7db42b6e9df1 100644
--- a/pandas/tests/tseries/offsets/test_business_day.py
+++ b/pandas/tests/tseries/offsets/test_business_day.py
@@ -7,7 +7,6 @@
     timedelta,
 )
 
-import numpy as np
 import pytest
 
 from pandas._libs.tslibs.offsets import (
@@ -61,7 +60,6 @@ def test_with_offset(self):
 
         assert (self.d + offset) == datetime(2008, 1, 2, 2)
 
-    @pytest.mark.parametrize("reverse", [True, False])
     @pytest.mark.parametrize(
         "td",
         [
@@ -71,20 +69,15 @@ def test_with_offset(self):
         ],
         ids=lambda x: type(x),
     )
-    def test_with_offset_index(self, reverse, td, request):
-        if reverse and isinstance(td, np.timedelta64):
-            mark = pytest.mark.xfail(
-                reason="need __array_priority__, but that causes other errors"
-            )
-            request.node.add_marker(mark)
+    def test_with_offset_index(self, td):
 
         dti = DatetimeIndex([self.d])
         expected = DatetimeIndex([datetime(2008, 1, 2, 2)])
 
-        if reverse:
-            result = dti + (td + self.offset)
-        else:
-            result = dti + (self.offset + td)
+        result = dti + (td + self.offset)
+        tm.assert_index_equal(result, expected)
+
+        result = dti + (self.offset + td)
         tm.assert_index_equal(result, expected)
 
     def test_eq(self):