Finding the market price for each order at the time it was placed
This seems to work.

Use numpy.searchsorted() to get the indices of the BBA for each order.  Add the indices as a new column to the order1 dataframe.  It's like bisect in the standard library.

Then merge the two dataframes on the insideMarke1 index and the order1 'BBA Index' column.

import pandas as pd
import numpy as np

insideMarke1 = pd.DataFrame({'Timestamp':['2019-12-01 08:00:00.123456', '2019-12-01 08:00:01.123456', '2019-12-01 08:00:02.123456', '2019-12-01 08:00:03.123456', '2019-12-01 08:00:05.123456'],
                             'bestBidQnt':[100, 100, 50, 50, 100],
                             'bestBidPrice':[50.01, 50.01, 50.02, 50.02, 50.01],
                             'bestAskPrice':[51.00, 50.99, 50.99, 50.50, 50.50],
                             'bestAskQnt':[200, 100, 100, 200, 200]})

orders1 = pd.DataFrame({'Entry Date and Time':['2019-11-30 17:29:50.000000','2019-12-01 07:30:01.112233', '2019-12-01 08:00:00.123456', '2019-12-01 08:00:00.512341', '2019-12-01 08:00:01.123456', '2019-12-01 08:00:02.123456', '2019-12-01 08:00:02.987654', '2019-12-01 08:00:03.123456', '2019-12-01 08:00:04.000000', '2019-12-01 08:00:05.123456'],
                       'Bid':['True', 'True', 'False', 'False', 'False', 'True', 'True', 'False', 'True', 'True'],
                       'Price':[49.00, 49.50, 51.00, 51.50, 50.99, 50.02, 48.00, 50.50, 49.00, 50.01 ],
                       'Qnt':[50, 100, 200, 150, 100, 50, 10, 200, 80, 100 ]})


insideMarke1[['Timestamp']] = insideMarke1[['Timestamp']].apply(pd.to_datetime, unit='ns') 
orders1[['Entry Date and Time']] = orders1[['Entry Date and Time']].apply(pd.to_datetime, unit='ns')

BBA_Index = np.searchsorted(insideMarke1['Timestamp'], orders1['Entry Date and Time'], 'left')
orders1['BBA Index'] =  (BBA_Index - 1).clip(0, len(insideMarke1))

orders1Complete = insideMarke1.merge(orders1, left_index=True, right_on='BBA Index')


result:

    Timestamp   bestBidQnt  bestBidPrice    bestAskPrice    bestAskQnt  Entry Date and Time     Bid     Price   Qnt     BBA Index
0   2019-12-01 08:00:00.123456  100     50.01   51.00   200     2019-11-30 17:29:50.000000  True    49.00    50     0
1   2019-12-01 08:00:00.123456  100     50.01   51.00   200     2019-12-01 07:30:01.112233  True    49.50   100     0
2   2019-12-01 08:00:00.123456  100     50.01   51.00   200     2019-12-01 08:00:00.123456  False   51.00   200     0
3   2019-12-01 08:00:00.123456  100     50.01   51.00   200     2019-12-01 08:00:00.512341  False   51.50   150     0
4   2019-12-01 08:00:00.123456  100     50.01   51.00   200     2019-12-01 08:00:01.123456  False   50.99   100     0
5   2019-12-01 08:00:01.123456  100     50.01   50.99   100     2019-12-01 08:00:02.123456  True    50.02    50     1
6   2019-12-01 08:00:02.123456   50     50.02   50.99   100     2019-12-01 08:00:02.987654  True    48.00    10     2
7   2019-12-01 08:00:02.123456   50     50.02   50.99   100     2019-12-01 08:00:03.123456  False   50.50   200     2
8   2019-12-01 08:00:03.123456   50     50.02   50.50   200     2019-12-01 08:00:04.000000  True    49.00    80     3
9   2019-12-01 08:00:03.123456   50     50.02   50.50   200     2019-12-01 08:00:05.123456  True    50.01   100     3