Docking Attribute Table using PyQgis
There is the setting Open attribute table in a dock window
which automatically opens the attribute table in the bottom dock window. You can set this manually via the menubar:
Settings > Options > Data Sources > Open attribute table in a dock window
Or via PyQGIS:
from PyQt4.QtCore import QSettings
QSettings().setValue("/Qgis/dockAttributeTable", True)
To do this in Qgis 3.x (expanding on the accepted answer by @Joseph), use:
from qgis.PyQt.QtCore import QSettings
QSettings().setValue("/Qgis/dockAttributeTable", True)
# And to check the current value of the setting
QSettings().value("/Qgis/dockAttributeTable")