Police don't encourage the public to take things into their own hands, and will always say you should leave it up to them. It's a shame the bike didn't "fall" over on his leg during the struggle. It could have pinned him nicely. I'd like to say good try Wattie, but I can't.
I just read this post and I know it's lengthy. There's some common logic points below. If your too lazy, don't bother. If you want to know some points on how to help then read on.
Like I said above, it is preferred by police that individuals don't get involved in a confrontation. It should be obvious that these people don't follow the same moral or ethic standards as the rest of us. You don't know what weapon they're carrying with them, what fighting experience they have, or what they're on, and you can bet your left nut that they are more desperate and motivated to keep themselves out of trouble than you are when your trying to get them into it.
Just a note to anyone that may recognise any stolen bike. Get straight on to 000, it's the quickest way to get any response. Don't call the local station thinking things will move faster. Your actually adding a 'middle man' into the mix (in Victoria anyway). If you call 000, they take the info and pass it directly onto the people on the ground. If you call the local station they take the info and relay it onto 000, who then have to collect the info from the station member, then repeat everything to the troops on the ground. It takes longer, and sometimes minutes count. (Like if your trying to catch a turd with a stolen motorcycle on the hop).
Take note of as much detail as you can. Get the plate number. If it's still the same, or another stolen one then so be it, but you never know what might come out of it (some of these people are not that smart) If you've seen them talking to somebody in another car get the rego of the car as well.
If you know a shop they have just been in, an address they attended, know where they have come from or have seen which way they were heading write it down. Also, Crooks need petrol too but unless someone knows the vehicle is stolen they'll go in and out of petrol stations all day, be recorded on cctv, and not draw attention to themselves.
DESCRIPTIONS PEOPLE!!! Get on it!! It's frustrating asking someone for a basic description such as "what colour hair" and having people say "......yeah......i don't know". Really? Because you just told me you were in a stand up, face to face argument for like 5 mins, and your telling me you can't remember if he was friggin blonde or brunnette.

Descriptions are gold, especially scars, tattoos or other marks. If any crook has any from you can bet your sweet ass that the police have their scars and tattoos recorded. In the heat of the moment it might prove difficult, but try any way.
Sometimes crooks leave the dumbest shit lying about OR sometimes if they are in a hurry or involved in a struggle for some odd reason (like being attacked by a vigilante motorcycle enthusiast ninja kickboxer) they'll drop shit. Or during the struggle you might find that something of theirs has ended up in your possession somehow

If you get your hands on anything of theirs, like a phone, wallet, bank card or anything, hand it over. It might be a lead to the identitiy directly, or might have good fingerprints on it. Just remember, police prefer you don't get involved in any confrontation.
If they touch anything shinny or smooth, like your helmet, while your attempting to reverse spinning heal kick them to the head, take it into the station but understand that some times it just doesn't work as well as CSI might let you believe.
Police can't get the description, location, diet and centrelink details from a single strand of hair, that's bullshit, BUT more and more criminals are being DNA profiled everyday, so you never know.
If for some reason you confront a crook and explain to them that he is on a stolen bike then they might attack you. That's assault. If they happen to push you over while your attempting your best Bruce Lee flying axe kick maneuver and you fall and hurt yourself, report it to police. Then, when shit bag goes to court for the handle stolen goods, there'll also be other assault related charges attached. I'll say it again, police prefer you don't get involved in any confrontation.
I said handle stolen goods for the following reason. Just because someone has been found in possession of the property doesn't prove they actually stole it. Don't be discouraged when you hear that they are charged with handle instead of theft. The handle charges have just as much punch as the thefts themselves.
If you have seen or been involved in anything, write it all down asap. Write down every detail that you can recall. Where you were, the time/date, all the details. If anyone else has witnessed any thing, try to get their details as well even if it's just a name and phone number. They might have noticed something you missed.
Disclaimer: I don't know every thing. I might be wrong. I'm not advising or encouraging any one to do any thing. Hot chips are better with vinegar. I'm not taking responsibility for people actions after reading this post.