I recommend you learn a bit about table styles. They can be very complex but it is necessary because, as you have discovered, the table style can override the styles applied to the text in the table. The bolding may not apply to the entire table, often it is because you have a first row or first column highlight turned on. This macro can be used to apply styling to all selected tables
Code:
Sub TableStyler()
Dim aTbl As Table
For Each aTbl In Selection.Tables
aTbl.Style = "My Table Style"
aTbl.ApplyStyleFirstColumn = False
aTbl.ApplyStyleRowBands = False
aTbl.Range.Style = "Table Text" 'paragraph style for all of table
aTbl.Rows(1).Range.Style = "Table Heading" 'paragraph style for first row
aTbl.PreferredWidthType = wdPreferredWidthAuto
aTbl.PreferredWidth = 100
Next aTbl
End Sub