Tie the knot is an old one (is it the Orthodox Greeks who still do it in the ceremony?).
Jump the broom (originated in slavery times, but I have heard whites say it about getting married.

Tie my bonnet- Haven't heard it applied to marriage and not in my slang or historical usage books. A mistake for tying apron strings?

Some other usages (all American; I don't have UK references except the Oxford English Dictionary):

To bonnet- hit someone over the head
To bonnet- to pull the wool over someone's eyes (hoodwink)
To have a bee in one's bonnet
He was off his bonnet (wrong, or insane)
Here's your bonnet- (get out!)
Keep it under your bonnet (don't talk about it)
He blew his bonnet
etc.

Closest I found is- The place where one hangs his bonnet, i. e. one's home and family.

Digression: In the late 18th c., "old hat" originated with reference to a woman's privates- because they were so often felt. From Grose, Dictionary of the Vulgar Tongue, ca. 1785.

Many other meanings to bonnet, but they don't apply to headgear (Decoy, assistants in a gambling establishment, an addition to a sail, ---).