This is a complex issue, and here is the simplest response I can give.
The web page you reference states clearly at the top "You cannot claim your car expenses from home to work". The exception is conferences, which are differentiated by a number of factors:
A) Not held at usual place of work;
B) Involve additional irregular travel expenes, and accomodation;
C) Involve related, but different duties to those day to day tasks of work.
So the question arises, "Can attending a race be classified as a conference?"
This is a spurious conclusion to draw at best. Regualar racing events don't count since it would be viewed as your regular place of work. Other less frequent racing venues would probably also fail the test since there are no conference activities occurring. Just regular work - bike racing.
However, let's humour you Mike, and assume that you are entitled to claim a tax deduction for your travel to your races, as long as you also include any race winnings as assessible income.
This will mean that either:
A) Your winnings will be greater than your tax deductible costs and you will pay tax on the net income at your marginal rate.
B) Your travel expenses will be greater than your winnings. You wil pay no tax on your winnings, and any losses can be carried forward and be offset against any future race wins.
You cannot claim any losses from (B) against other income you earn. Before arguing with me on this, I suggest you read what the ato has to say about Non-Commercial Losses
here.
The tax office already allows bike racing to be treated as a hobby. This means that you don't get to claim expenses for the hobby, but you don't have to account for any winnings either. This is a much simpler solution, that gives the same result (or better!), but without the hassles of all the additional paperwork.