Phones and tablets are all about swipes.
Going throught menu is not user friendly.
So I suggest to quick access TABS with a swipe from the left side of the screen.
And quick access BOOKMARKS with a swipe form the right side of the screen.
This is an elegant and effective way to access the most used functionailties.
Ps.: This way of access TABS and BOOKMARKS already implemented other browser (example: Lighting Browser Android), so anyone can test this UI.