Yes, in almost all cases you can get your records out without retyping them. The reporting area of the software normally lets you pull bookings for a chosen date range and download them as a spreadsheet file, with the passenger names, travel dates, supplier, booking reference and the amounts collected. Your bookkeeper can then bring that file into most common accounting packages, which is how a lot of agencies handle it.
Whether it goes across automatically, without anyone downloading anything, is a different matter and depends on your plan and on what your accounting package will accept. A direct link that sends each booking over as soon as it is made is extra work to set up and is not part of every arrangement, so please ask about it rather than assume it is already there. A plain download and upload, on the other hand, is something you should expect to have.
One honest warning is that the column names in the download will rarely match what your accounting software expects on the first try, so somebody usually has to map the fields once at the start. After that it tends to be straightforward. How much cost detail appears also depends on the supplier, because some return their net rate to you and some only return a selling price, and the software can only pass on what it is given.
The sensible next step is to pull one month of bookings, send that file to whoever does your books, and ask them which columns they actually need before you settle on a routine.