diff --git a/doc/source/whatsnew/v1.2.0.rst b/doc/source/whatsnew/v1.2.0.rst
index 7c850ffedfcab..281edf1834fb2 100644
--- a/doc/source/whatsnew/v1.2.0.rst
+++ b/doc/source/whatsnew/v1.2.0.rst
@@ -390,6 +390,7 @@ Datetimelike
 - Bug in :meth:`DatetimeIndex.equals` and :meth:`TimedeltaIndex.equals` incorrectly considering ``int64`` indexes as equal (:issue:`36744`)
 - Bug in :meth:`TimedeltaIndex.sum` and :meth:`Series.sum` with ``timedelta64`` dtype on an empty index or series returning ``NaT`` instead of ``Timedelta(0)`` (:issue:`31751`)
 - Bug in :meth:`DatetimeArray.shift` incorrectly allowing ``fill_value`` with a mismatched timezone (:issue:`37299`)
+- Bug in adding a :class:`BusinessDay` with nonzero ``offset`` to a non-scalar other (:issue:`37457`)
 
 Timedelta
 ^^^^^^^^^
diff --git a/pandas/_libs/tslibs/offsets.pyx b/pandas/_libs/tslibs/offsets.pyx
index 98b2ddbd21ee1..dbd094905cf24 100644
--- a/pandas/_libs/tslibs/offsets.pyx
+++ b/pandas/_libs/tslibs/offsets.pyx
@@ -1388,7 +1388,11 @@ cdef class BusinessDay(BusinessMixin):
     @apply_array_wraps
     def _apply_array(self, dtarr):
         i8other = dtarr.view("i8")
-        return shift_bdays(i8other, self.n)
+        res = _shift_bdays(i8other, self.n)
+        if self.offset:
+            res = res.view("M8[ns]") + Timedelta(self.offset)
+            res = res.view("i8")
+        return res
 
     def is_on_offset(self, dt: datetime) -> bool:
         if self.normalize and not _is_normalized(dt):
@@ -3778,7 +3782,7 @@ cdef inline void _shift_quarters(const int64_t[:] dtindex,
         out[i] = dtstruct_to_dt64(&dts)
 
 
-cdef ndarray[int64_t] shift_bdays(const int64_t[:] i8other, int periods):
+cdef ndarray[int64_t] _shift_bdays(const int64_t[:] i8other, int periods):
     """
     Implementation of BusinessDay.apply_offset.
 
diff --git a/pandas/tests/tseries/offsets/test_offsets.py b/pandas/tests/tseries/offsets/test_offsets.py
index 922aff1792227..fba123e47feb2 100644
--- a/pandas/tests/tseries/offsets/test_offsets.py
+++ b/pandas/tests/tseries/offsets/test_offsets.py
@@ -750,6 +750,13 @@ def test_with_offset(self):
 
         assert (self.d + offset) == datetime(2008, 1, 2, 2)
 
+    def test_with_offset_index(self):
+        dti = DatetimeIndex([self.d])
+        result = dti + (self.offset + timedelta(hours=2))
+
+        expected = DatetimeIndex([datetime(2008, 1, 2, 2)])
+        tm.assert_index_equal(result, expected)
+
     def test_eq(self):
         assert self.offset2 == self.offset2
 
@@ -2642,6 +2649,13 @@ def test_with_offset(self):
 
         assert (self.d + offset) == datetime(2008, 1, 2, 2)
 
+    def test_with_offset_index(self):
+        dti = DatetimeIndex([self.d])
+        result = dti + (self.offset + timedelta(hours=2))
+
+        expected = DatetimeIndex([datetime(2008, 1, 2, 2)])
+        tm.assert_index_equal(result, expected)
+
     def test_eq(self):
         assert self.offset2 == self.offset2