I also love the character ! and nice size bathroom. The sink and toilet look like Kohler 'Memoirs' series and look perfect with the tub which looks original ? The floor looks appropriate with the white tile.
The beige travertine definitely looks out of place - pull it out carefully and find another use for the stone. A glass shower door or even a shower curtain would look more in keeping with the age. Try softening and coordinating the room with fabric - curtains, rugs towels. Find a print that includes at least that blue, gray and white (and maybe more colors) for curtains. Then select a pale wall paint in a color chosen from the curtain fabric. ( blue, grey as in the floor or other. It will make a world of difference for you. If you really don't like the blue tile, replace just those tiles with more of the white or perhaps the grey in the floor to keep all hard surfaces neutral. Where the grab bars are, you can remove and replace those tiles or grout that have been drilled or remove bars, patch and touch up with a porcelain paint until later changes allow. Some hand-held showers also utilize the vertical bar type to hold the head. Question of the day - How did that poor woman ever reach the TP without falling off her seat ? I see the radiator, but maybe a free-stander would work ?