To me, this is nothing different than when a runner inadvertently contacts a loose ball on the field. These include a batted ball that a fielder deflected, a loose ball that a fielder failed to catch (e.g., F4 drops F2's throw on a steal of second base, and the runner slides into the ball, kicking it into the outfield), etc. No foul, play on.
Interference by a BR is covered under 8-2-E thru H. There is nothing there that talks of interfering with a loose ball except for a dropped third strike, when the batter-runner is liable to be put out. This was a walk, so she is awarded first base; there's no possibility to make a play on her going to first.