diff --git a/doc/source/whatsnew/v1.4.0.rst b/doc/source/whatsnew/v1.4.0.rst
index 99a66c7e5454b..8732e1c397ce5 100644
--- a/doc/source/whatsnew/v1.4.0.rst
+++ b/doc/source/whatsnew/v1.4.0.rst
@@ -579,6 +579,7 @@ I/O
 Period
 ^^^^^^
 - Bug in adding a :class:`Period` object to a ``np.timedelta64`` object incorrectly raising ``TypeError`` (:issue:`44182`)
+- Bug in :meth:`PeriodIndex.to_timestamp` when the index has ``freq="B"`` inferring ``freq="D"`` for its result instead of ``freq="B"`` (:issue:`44105`)
 -
 
 Plotting
diff --git a/pandas/core/arrays/period.py b/pandas/core/arrays/period.py
index 2f36b72229225..01018c7263f32 100644
--- a/pandas/core/arrays/period.py
+++ b/pandas/core/arrays/period.py
@@ -12,6 +12,7 @@
 
 import numpy as np
 
+from pandas._libs import algos as libalgos
 from pandas._libs.arrays import NDArrayBacked
 from pandas._libs.tslibs import (
     BaseOffset,
@@ -506,7 +507,22 @@ def to_timestamp(self, freq=None, how: str = "start") -> DatetimeArray:
         new_parr = self.asfreq(freq, how=how)
 
         new_data = libperiod.periodarr_to_dt64arr(new_parr.asi8, base)
-        return DatetimeArray(new_data)._with_freq("infer")
+        dta = DatetimeArray(new_data)
+
+        if self.freq.name == "B":
+            # See if we can retain BDay instead of Day in cases where
+            #  len(self) is too small for infer_freq to distinguish between them
+            diffs = libalgos.unique_deltas(self.asi8)
+            if len(diffs) == 1:
+                diff = diffs[0]
+                if diff == self.freq.n:
+                    dta._freq = self.freq
+                elif diff == 1:
+                    dta._freq = self.freq.base
+                # TODO: other cases?
+            return dta
+        else:
+            return dta._with_freq("infer")
 
     # --------------------------------------------------------------------
 
diff --git a/pandas/tests/arrays/test_datetimelike.py b/pandas/tests/arrays/test_datetimelike.py
index c7c1ce6c04692..13fe3c2d427c5 100644
--- a/pandas/tests/arrays/test_datetimelike.py
+++ b/pandas/tests/arrays/test_datetimelike.py
@@ -1114,6 +1114,25 @@ def test_to_timestamp(self, how, arr1d):
         #  an EA-specific tm.assert_ function
         tm.assert_index_equal(pd.Index(result), pd.Index(expected))
 
+    def test_to_timestamp_roundtrip_bday(self):
+        # Case where infer_freq inside would choose "D" instead of "B"
+        dta = pd.date_range("2021-10-18", periods=3, freq="B")._data
+        parr = dta.to_period()
+        result = parr.to_timestamp()
+        assert result.freq == "B"
+        tm.assert_extension_array_equal(result, dta)
+
+        dta2 = dta[::2]
+        parr2 = dta2.to_period()
+        result2 = parr2.to_timestamp()
+        assert result2.freq == "2B"
+        tm.assert_extension_array_equal(result2, dta2)
+
+        parr3 = dta.to_period("2B")
+        result3 = parr3.to_timestamp()
+        assert result3.freq == "B"
+        tm.assert_extension_array_equal(result3, dta)
+
     def test_to_timestamp_out_of_bounds(self):
         # GH#19643 previously overflowed silently
         pi = pd.period_range("1500", freq="Y", periods=3)