I had HDR so can't really compare. For what it's worth I had no real discomfort from that procedure and could have been back on a bike in days.
They will be positioning your seeds carefully and you don't want them moving about. So I would be quite cautious of being on a bike.
The seeds have a half life depending on the isotope used I think this can be anything from 10 days to 60 days. After 4 half lives the seeds will have delivered more than 90% of the radiation dose and personally if the other 10% wasn't quite delivered in the right place I wouldn't be bothered.
So if you were being really cautious find out the half life of the seeds and multiply by 4. If the seeds get locked in place by scar tissue after perhaps a month then I guess it would be safe to be back in the saddle then.
I'm very much a leisure cyclist, for me missing 40 days of cycling would be no problem, and missing 240 days wouldn't be an issue, but I have other hobbies and if some one said you can't play the violin for 9 months I wouldn't be happy, but if they said you'll die of cancer unless you stop playing for 9 months then I would stop. Anyone who has heard my violin playing would have been glad of the nine month break.