"But your Mum and Dad…” said Harry, pushing against the barrier again in the vain hope that it would give way. “How will they get home?”
“They don’t need the car!” said Ron impatiently. “They know how to Apparate! You know, just vanish and reappear at home! They only bother with Floo powder and the car because we’re all underage and we’re not allowed to Apparate yet.…”
Chamber of Secrets, chapter 5
This is when Harry and Ron begin to make the decision that they should steal the car to get to Hogwarts. When Ron says "they" this could be interpreted as they can both apparate or they will both be apparating. One version has Molly and Arthur disapparating separately the other has them disapparating together through side along apparation.
There is yet more evidence, but sadly this too could be construed as side along.
But Mrs. Weasley only smile and waved. Before the train had rounder the corner, she, Bill and Charlier had Disapparated
Goblet of Fire
Aside from actual quotes it is possible to infer from Pottermore and her general life that she can Apparate.
Wizards who cannot Apparate (dematerialise and reappear at will), who wish to travel by daylight (meaning that broomsticks, Thestrals, flying cars and dragons are inappropriate), or whose destination has no fireplace (rendering Floo powder useless) will have to resort to the use of a Portkey.
Pottermore - Portkeys
Now throughout her 30 (Bill was born in 1970) or so years of being a stay at home mum it is exceedingly likely that at at least one point in time she would need to travel somewhere during daylight that does not have a fireplace.
