What if Grandma C has been telling the truth all along? That Elizabeth usually stuck close to home when she was biking.
If that was true, then Grandma C might have seen the cousins at 12:15 pm and then glanced out again around 12:20 pm, expecting to see them.
She doesn't see them at 12:20 pm, so she starts keeping a continuous eye on the street. Maybe she calls them, no response. Five more minutes go by, another five and it's clear that the girls must have gone further than they were allowed to go.
So Grandma C tells Elizabeth's 12 year old brother to keep an eye on his two younger sisters, hops in her car and starts looking for the girls.
In other words, maybe Grandma C really did keep a close eye on the girls (contrary to what many posts in these threads have posited). And when they were gone longer than could be explained by a zip around the block, she got worried and started looking for the girls.