Very nice Mixte.

I know it says Bob Jackson on the frame but the logo on the front - is that Raleigh?

One of my bikes is a Raleigh Mixte frame too (the one in the avatar), the only difference is she has dropped handlebars and I wear whatever I like on her depending on our changeable British weather. Sometimes I wear lycra, sometimes leggings (tights), sometimes a pair of tight-legged jeans I have - and always my helmet and gloves.

I'd say wear whatever you're comfortable in and enjoy your bike