Bat in the way

[streamdoc]

R1 on 3rd, Batter hits a grounder to the infield. Fielder throws home to try to get the runner coming in from 3rd. Batter dropped her bat in the left side batter's box, in the baseline, about 1 foot on the 3rd base side of home plate (bat is in a place that would make it impossible for her to slide, and touch the plate without hitting the bat). R1 decides not to slide, I assume because she felt that the bat was in her way - R1 steps over the bat, and touches the plate ahead of the tag. Pitcher immediately complains, stating that the runner "has to slide". I know that this is not true, but here is my theoretical question. Let's assume that the runner did not slide, and was tagged out. Is there any call regarding the bat being in the way (I assume not, but just want to check)? Also, do you fellow umps try to get the bat out of the baseline prior to the runner reaching the area if possible? I've seen, and done it myself - a quick kick of the bat into fout territory if there is time.