There could be a connection to the Bibey family who were living in and around the English Bicknor area during the 1700's and into the 1800's. The name is spelt many different ways in the Parish records.

Averil Cave

There are these on FreeBMD (plus a few from other areas):

Marriages Sep 1849 (>99%)

Bibe William Ross 26 291

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Births Dec 1849 (>99%)

BIBE Leah Monmouth 26 76

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Births Jun 1853 (98%)

Bibe Richard Ross 6a 411

There are also 15 records on this site for Bibe

Year: 1824
Month: Oct
Day: 31
Parents Surname: BROBYN
Child Forenames: Isabella
Father's Forenames: Edward
Mother's Forenames: Mary
Mother's Surname:
Place of Residence: Newnham
Occupation: Waterman
Officiating Minister: J D [illegible] Off[iciatin]g Minister
Event type: Baptism
Memoranda: D[aughter] of
Notes:
Register Reference: P228 IN 1/5
Page No: 51
Parish_Chapel: Newnham

Year: 1826
Month: Dec
Day: 3
Parents Surname: CLEMENTS
Child Forenames: Samuel
Father's Forenames: Giles
Mother's Forenames: Elizabeth
Mother's Surname:
Place of Residence: Westbury
Occupation: Labourer
Officiating Minister: William Crawley
Event type: Baptism
Memoranda:
Notes:
Register Reference: P354 IN 1/6
Page No: 103
Parish_Chapel: Westbury on Severn

1841 Elton
Giles Clemmens abt 1801 Gloucestershire, England Westbury On Severn, Gloucestershire
Elizabeth Clemmens abt 1801 Gloucestershire, England Westbury On Severn, Gloucestershire
Edwin Clemmens abt 1833 Gloucestershire, England Westbury On Severn, Gloucestershire
Joseph Clemmens abt 1821 Gloucestershire, England Westbury On Severn, Gloucestershire
William Clemmens abt 1816 Gloucestershire, England Westbury On Severn,

1841
Edward Bricken abt 1776 Gloucestershire, England Newnham, Gloucestershire
Mary Bricken abt 1786 Gloucestershire, England Newnham, Gloucestershire
Amelia Bricken abt 1829 Gloucestershire, England Newnham, Gloucestershire
Caroline Bricken abt 1818 Gloucestershire, England Newnham, Gloucestershire
Isabella Bricken abt 1825 Gloucestershire, England Newnham, Gloucestershire
Sophia Bricken abt 1823 Gloucestershire, England Newnham, Gloucestershire

Name: Isabella Brobbin
Name: Samuel Clements
Year of Registration: 1845
Quarter of Registration: Jul-Aug-Sep
District: Westbury On Severn
County: Gloucestershire
Volume: 11
Page: 635

1851 Broad Street
Samuel Clements abt 1829 Westbury, Gloucestershire, England Head Little Dean, Gloucestershire
Isabella Clements abt 1828 Newnham, Gloucestershire, England Wife Little Dean, Gloucestershire
Enoch Clements abt 1846 Littledean, Gloucestershire, England Son Little Dean, Gloucestershire
Harriot Clements abt 1848 Newnham, Gloucestershire, England Daughter Little Dean, Gloucestershire
Samuel Clements abt 1850 Newnham, Gloucestershire, England Son Little Dean, Gloucestershire
Edwin Clements abt 1835 Littledean, Gloucestershire, England Brother Little Dean, Gloucestershire

Name: Bibbie Clements
Year of Registration: 1856
Quarter of Registration: Jan-Feb-Mar
District: Westbury On Severn
County: Gloucestershire
Volume: 6a
Page: 191

Year: 1856
Month: Feb
Day: 24
Parents Surname: CLEMENTS
Child Forenames: Henry Bib(?)
Father's Forenames: Samuel
Mother's Forenames: Isabella
Mother's Surname:
Place of Residence: East Dean
Occupation: Labourer
Officiating Minister: T. M. Wetherell
Event type: Baptism
Memoranda:
Notes:
Register Reference: P 145 IN 1/7
Page No: 41
Parish_Chapel: Flaxley

Year: 1857
Month: Oct
Day: 25
Surname: CLEMENTS
Forenames: Henry Biley
Place of Residence: Popes Hill
Age at death: one year
Officiating Minister: J.G.Smythies
Event: Burial
Cause of death:
Memoranda:
Notes:
Register Reference: P85/1 in 1/12
Page No: 33
Parish_Chapel: Cinderford St Johns

Then your Henry

Year: 1858
Month: Apr
Day: 19
Parents Surname: CLEMENTS
Child Forenames: Henry Bib(?)
Father's Forenames: Samuel
Mother's Forenames: Isabella
Mother's Surname:
Place of Residence: East Dean
Occupation: Labourer
Officiating Minister: T. M. Wetherell
Event type: Baptism
Memoranda: Priv. Recd into Ch. May 16
Notes:
Register Reference: P 145 IN 1/7
Page No: 44
Parish_Chapel: Flaxley

1861
Samuel Sements abt 1826 Elton; Westbury On Serven, Gloucestershire, England Head Littledean, Gloucestershire
Isabella Sements abt 1827 Newnham, Gloucestershire, England Wife Littledean, Gloucestershire
Enoch Sements abt 1847 Westbury On Severn, Gloucestershire, England Son Littledean, Gloucestershire
Harriett Sements abt 1849 Popar Hill East Dean, Gloucestershire, England Daughter Littledean, Gloucestershire
Henry Sements abt 1858 Popar Hill East Dean, Gloucestershire, England Son Littledean, Gloucestershire
John Sements abt 1860 Popar Hill East Dean, Gloucestershire, England Son Littledean, Gloucestershire
Samuel Sements abt 1855 Popar Hill East Dean, Gloucestershire, England Son Littledean, Gloucestershire

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Ἀριστοτέλης A Gloster Boy in the Forest of Dean ><((((*>