You'll be fine taking the roadway up on foot, but if you take the steep route through the archway, wear sensible non-slippy shoes. It is eas to turn your ankle on this route. We choose not to come back down this way as it was so slippy.
If it's not bears, it's wasps. There were hundreds of them on the hill and around the castle at the end of August. I nearly stepped on at least one nest that was built into the steps up to the castle. Some of them can be really annoying. I suggest wearing peppermint oil and carrying a small can of wasp killer with you.