Can I stop my new staff from seeing everything in the system and only let them handle bookings?

Yes, in most cases you can. Travel agency software is normally set up so that every person who works for you gets their own login, and each login is given a role that decides what they can open and what stays hidden. So a new member of staff can be allowed to search, quote and make bookings while the parts of the system you would rather keep to yourself stay out of reach.

In practice that usually means a junior login can see the booking screens and the customer they are working with, but not your markup settings, your supplier connections, your sales and profit reports, or the screens where money is refunded. You can also often limit a person to the bookings they made themselves, rather than everything the whole office has done, which is useful if you have several agents working side by side. Changing someone's role later is normally just a matter of editing their user record, and you can switch a login off entirely on the day somebody leaves.

How finely you can slice this does depend on the system and on your plan. Some setups give you ready made roles such as agent, accounts and administrator, and you choose the closest fit rather than ticking each permission one by one. It is also worth knowing that if a role can see a booking at all, it may see the net cost on that booking, so ask specifically about hiding cost and commission if that matters to you.

Before your new person starts, ask to see the list of roles available to you and what each one can and cannot do, then create a test login with that role and click through it yourself so there are no surprises.