Is your bun and indoor or outdoor bun?
When both our buns got fixed (male (Rolo) and female (Taffy), separate time periods) we kept them indoors for a couple of days prior to their surgery. This allowed them to become comfortable and happy with their new environment so that it wasn’t adding extra stress to them post-surgery. They didn’t go back outside for a least a week after surgery – as our summers are generally mild rather than hot, room temperature and outdoor temperature are fairly similar so it’s easier for them to adapt.
Post-surgery we took out anything that could be jumped on. I suspect as the surgery is pretty invasive she will be in a fair degree of pain so probably won’t want to jump on anything anyway, however, it does eliminate that potential risk of splitting her cut upon jumping should she try it. All we had in our buns’ run during both of their recoveries was a few light blankets covering the whole floor area so they were comfortably warm, their food & water bottles / bowls, litter tray and a couple of items to chew on. We cleaned the litter tray fully on a daily basis, normally we spot check their litter areas in their hutch but it should eliminate the risk of infection.***
Our vet didn’t provide our Taffy with a cone – to be honest I didn’t even realise they existed for rabbits – however, Rolo was given one. If she is given a cone I would keep a strong eye on whether it stresses her too much. Rolo pulled his off within 30 seconds of us returning home and wouldn’t allow me to put it back on; in honesty, I think him having the cone on would have stressed him out more than it would have benefited him so would have only prolonged the healing process. I think not having a cone is fine as long as she isn’t pulling at her stitches; I believe the stitches are generally left on the inside and disintegrate – alternatively, they could use glue.
Ultimately, pre-surgery and post-surgery should be used to keep your bun as happy and comfortable as possible, certainly post-surgery. Keep everything routine in regards to food leading up to and directly after surgery, remove hazards etc. Just ensure your bun is kept in a comfortably warm environment and that it is quiet after surgery. We put our buns’ runs in our room and closed the door completely. She is likely going to be doing a lot of laying around and teeth grinding from our own personal experience so it’s best to leave her be, just ensure she is eating and drinking regularly – this might be infrequent initially but as long as she is doing this within 24 hours (I believe this is the cut off time) she should be okay, if not, give the vet a call. We were given a syringe and a pellet based paste to try to feed Taffy if she didn’t eat; we didn’t find it particularly useful but it did add an extra layer of security to try and feed Taffy. We checked her cut every 4-6 hours, although daily may be suffice.
Good luck!
EDIT
***didn’t realise BunN also recommended not letting your bun jump on anything too, but I definitely second it!
(On a side note, I would recommend asking your vet to check your buns teeth and nails too whilst you’re there – our vet did this for free as she was operating on both Taffy and Rolo anyway).