You can always use a large industrial plunger in the toilet pan. Its usually green and costs about £20 you can buy it from drainage center b & q sometimes sell it to well worth the money. I would defiantly check the drain before you call out a company as they charge you by the half an hour and...
Sorry to disappoint but there are no top access bath wastes in circulation. Shower traps are slightly larger diameter on top and you would not get a sufficient seal underneath your bath.
Joe