I think you need to have a heart to heart with your dh.
It used to be difficult between dh, ds and i with activities. Ds would do what i referred to as 'statutory moaning' before any activity, and it was rubbish and drained a lot of the joy. But my goal was to get him out, not going out wasn't an option. Sometimes it could take 30 minutes and he's neurotypical. Dh was chrinically ill but was just unable to take it - except on very rare occasions he just used to give in. Only a few years ago i discovered he also found it painful to listen to me sparring verbally with ds during the moaning period. It really was just joking and i don't think ds was upset by it, but perhaps it was more argumentative than it needed to be. I took that on board and tried to be gentler. But my message always was , the sooner we go, the sooner it will finish, but this is going to happen. I felt so let down by dh giving in, making me the bad cop again, teaching ds that if he fought hard enough he wouldn't have to go.
Your dh sees cycling as his me-time, his space, on his terms, perhaps to be kind his only break. Well, tough. Some of it has to be parent time now.
Between you, share how ds's reluctance and refusal makes you both feel - angry, out of control, scared for the future, frustrated, anxious? Share the goals - maybe 15- 30 mins time of activity outdoors, every day, no matter what it takes? and share strategies to try. It might be easier if you are elsewhere while your dh gets your ds to come with him. On the understanding that he DOES NOT give up, and if he is struggling he gets you to take over and has a breather before another go. Broken record, maybe? 'Cycling time, it'll be over soon?' Sorry if none of this works for asd but you must get on the same team about this.