Hi! Thank you for asking us, we are flattered :P
I am pretty sure visits for turist/ non-students are admitted. I will ask to some Oxonians so we’ll keep in touch, but there’s the information I currently have:
In general, access to college libraries is restricted to members of that college, and some other libraries impose restrictions on access to non-members of the department or faculty. Members are advised to consult the library guides for individual library policy.
Others, including non-members of Oxford University, should follow the links on these pages and complete the admissions form(s) for the Bodleian Libraries and consult individual library guides for other libraries.
I think they don’t talk about visits, just about using it, meaning taking books.
Here you are:
http://www.bodleian.ox.ac.uk/libraries/libraries?sq_content_src=%2BdXJsPWh0dHAlM0ElMkYlMkZ3d3cubGliLm94LmFjLnVrJTJGbGlicmFyaWVzJTJGZ3VpZGVzJTJGQk9ELmh0bWwmYWxsPTE%3D
Sorry for the late and no, we didn’t receive any ask yesterday, thank you for trusting us! By the way, are you planning a trip to the city too?