BUG: resample('B') ignores closed and label?

[MarcoGorelli]

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• I have checked that this issue has not already been reported.

• I have confirmed this bug exists on the latest version of pandas.

• I have confirmed this bug exists on the main branch of pandas.

Reproducible Example

In [64]: s = pd.Series([1, 2, 3, 4, 5, 6], index=pd.date_range('2023-09-26', periods=6, freq='12H'))

In [65]: s.resample('B', closed='left', label='left').mean()
Out[65]:
2023-09-26    1.5
2023-09-27    3.5
2023-09-28    5.5
Freq: B, dtype: float64

In [66]: s.resample('B', closed='right', label='right').mean()
Out[66]:
2023-09-26    1.5
2023-09-27    3.5
2023-09-28    5.5
Freq: B, dtype: float64

Issue Description

the two results are the same, but surely should differ?

Expected Behavior

In [3]: s = pd.Series([1, 2, 3, 4, 5, 6], index=pd.date_range('2023-09-26', periods=6, freq='12H'))

In [4]: s.resample('B', closed='left', label='left').mean()
Out[4]: 
2023-09-26    1.5
2023-09-27    3.5
2023-09-28    5.5
Freq: B, dtype: float64

In [5]: s.resample('B', closed='right', label='right').mean()
Out[5]: 
2023-09-26    1.0
2023-09-27    2.5
2023-09-28    4.5
2023-09-29    6.0
Freq: B, dtype: float64

Installed Versions

INSTALLED VERSIONS

commit : e86ed37
python : 3.10.12.final.0
python-bits : 64
OS : Linux
OS-release : 5.10.102.1-microsoft-standard-WSL2
Version : #1 SMP Wed Mar 2 00:30:59 UTC 2022
machine : x86_64
processor : x86_64
byteorder : little
LC_ALL : None
LANG : en_GB.UTF-8
LOCALE : en_GB.UTF-8

pandas : 2.1.1
numpy : 1.25.1
pytz : 2023.3
dateutil : 2.8.2
setuptools : 67.6.1
pip : 23.1.2
Cython : None
pytest : 7.3.1
hypothesis : 6.82.4
sphinx : None
blosc : None
feather : None
xlsxwriter : None
lxml.etree : None
html5lib : None
pymysql : None
psycopg2 : None
jinja2 : 3.1.2
IPython : 8.13.2
pandas_datareader : None
bs4 : 4.12.2
bottleneck : None
dataframe-api-compat: None
fastparquet : 2023.7.0
fsspec : 2023.6.0
gcsfs : None
matplotlib : 3.7.1
numba : None
numexpr : None
odfpy : None
openpyxl : None
pandas_gbq : None
pyarrow : 12.0.1
pyreadstat : None
pyxlsb : None
s3fs : None
scipy : 1.11.0
sqlalchemy : 2.0.20
tables : None
tabulate : None
xarray : None
xlrd : None
zstandard : None
tzdata : 2023.3
qtpy : None
pyqt5 : None
None