The simple way is to let Flash do the bitmap resampling for you. Rather than composing the scene with blitting, make a movable object an individual Bitmap added to a parent DisplayObject, give the Bitmap fractional x,y coordinates, and set its pixelSnapping to NEVER. (The default for pixelSnapping is AUTO, which means Flash will round to int coordinates when the Bitmap's scale is close enough to 1.0, which I think is for aesthetic reasons as well as performance.)
I don't know how fast this dynamic resampling will be in arbitrary conditions. You should try it for your case and see if it's fast enough. One complication: I think Flash will use the GPU for this when it can, so simple tests may be misleading.
The much-more-work-but-maybe-faster way is to precompute resampled Bitmaps, like for one Bitmap, generate 16 Bitmaps, one for every .25 pixel offset in the x/y directions, and then blit whichever one is closest to the subpixel position.