It is my understanding that "legitimate reason to travel" refers to the fact your travel is not an attempt to defeat creditors.
In the Bankruptcy Act the only reference I have found to travel so far is in Section 272 which states:
Leaving Australia with intent to defeat creditors etc.
(1) A person who:
(a) within 6 months before the presentation of the petition on or by virtue of which he or she became a bankrupt, left Australia, or did an act preparatory to leaving Australia, with intent to defeat or delay his or her creditors; or
(b) after the presentation of the petition on or by virtue of which he or she became a bankrupt and before he or she became bankrupt, left Australia, or did an act preparatory to leaving Australia, with intent to defeat or delay his or her creditors; or
(c) after he or she has become a bankrupt and before he or she is discharged from the bankruptcy, without the consent in writing of the trustee of his or her estate, leaves Australia, or does an act preparatory to leaving Australia;
is guilty of an offence and is punishable, on conviction, if the offence relates to the doing of a thing specified in paragraph (a) or (b), by imprisonment for a period not exceeding 5 years or, in any other case, by imprisonment for a period not exceeding 3 years.
Whilst your trustee may not know about it if you travel overseas on your British Passport, when or if they find out, you will be in trouble. Hence, best to obtain the trustee's permission before travelling. At the very least, give them a heads up notice.
You may also have a problem entering back into the country if you are bankrupt and traveling on your British Passport.
Also, if you are an Australian citizen and you try to leave Australia on a British passport, you will have no entry stamp because you reside here and I am guessing they would ask questions and want to see your Australian Passport?? You may also have difficulties coming back in here on your British - like you would need to be on a visa of some sort - unless you can prove you are an Australian resident.