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4) Be patient, and give suggestions - not commands. Don't bark at her to gear down or to keep her head up. Be nice for crying out loud, she is working her butt off for you!
5) Progressively try harder things. After a few times out, suggest a new trail that you think she is ready for now. The key is to tell her you have seen an improvement and that you think she'll really enjoy this one. Make sure to tell her that if at any point she doesn't like it you can stop (very important - it's likely that once she's in she'll be fine, but just knowing that it's okay to back out will make it less intimidating).
6) Tell her how much you are enjoying her company and how excited you are to try something she likes (don't worry, you don't actually have to go to the ballet - she may forget you mentioned it).
7) After the event take her out for a nice dinner or drink and tell her how hot you thought she looked climbing that hill, or trudging through the river even if it's a bald-face lie. Guaranteed second ride.
8) Wait three days before mentioning it again (not before calling her again - the three day rule is a myth), meaning don't ride her about it and hound her to go out again until she has had time to get the lactic acid out of her legs.
Everybody want to do things to make their significant others happy and proud. They are going to want praise for going with you and working hard. So even if she sucked, tell her how great it was. Even if she bitched non-stop (hey, some relationships just aren't gonna work out) tell her you had fun (and make a mental note to never ask her again). The key is to communicate how nice it was to spend time with her doing something you love. Tell her you want to help her get better, and maybe even buy her an uber-comfy seat.
To get what you want you have to work for it. Guys, if you want your new girlfriend to participate in your favorite sport you will need to be patient, be reassuring and be grateful. Push, but only push if she responds well to a challenge. Some of us do and some of us will hit you over the head with your air pump.