With reference to the fact that a roaring bull can be heard over a great distance, the Australian-English phrase within a bull’s roar of:
– means far away from when used negatively, particularly as not within a bull’s roar of;
– means not too far away from when used affirmatively.

The phrase within a bull’s roar of occurs, for example, in the following from Red slash across our green scorecard, by Ross Gittins, published in The Sydney Morning Herald (Sydney, New South Wales) of Wednesday 15^th August 2001:

I don’t usually assume that OECD economists are wiser and more knowledgeable than the home-grown variety just because they come from Paris. On this occasion, however, they’ve given us a far franker assessment of the inadequacy of our environmental effort than could any econocrat working within a bull’s roar of the Government.

The earliest occurrences of the phrase within a bull’s roar of that I have found are as follows, in chronological order:

1-: From the following advertisement, published in The Saturday Evening Express (Launceston, Tasmania) of Saturday 26^th July 1930:

AGAIN — AGAIN — AGAIN
THE TORPEDO SHOOTS HOME

The Torpedo shot home again last Saturday, with the force of a whirlwind; no other Bicycle could get within “a bull’s roar” of it, as results show—A. Rankin 1^st, and J. Royle 2^nd, last Saturday.
Call and Inspect the Cycle with a backbone of steel. Easy terms arranged.

CHAS. HAY’S CYCLE SHOP
9 INVERMAY ROAD
Agent for B.B.A. Motor Cycles. Try us for Repairs.

2-: From Smith’s Weekly (Sydney, New South Wales) of Saturday 20^th October 1934:

WHO’S AFRAID OF THE BIG BAD BULL?
ONCE again N.S.W. Premier Stevens is all square with Mr. Lang. Last time, B.S.B. followed J.T.L.’s idea of slimming; this time, “Tubby” has purchased a bull. Moreover, he has presented it to the Scheyville Training Farm, which is within a bull’s roar of Jack Lang’s prize pet.

3-: From news from Edith Creek, published in the Circular Head Chronicle (Stanley, Tasmania) of Wednesday 20^th March 1935:

Messrs. F. D. Hay & Sons’ sawmill at Roger River was again destroyed by fire in the early hours of Tuesday morning of last week, and it is a mystery how the fire originated, as there was no fire within a bull’s roar of the place.

4-: From Bob Inkson Tells How He Missed A Fortune on Nobility in G. N. Hurdle, by Bob Inkson, a former jockey, with J. M. Rohan, published in The Sporting Globe (Melbourne, Victoria) of Saturday 22^nd August 1936:

I remember in one of the steeples Agricolo won at Flemington, his price drifted after his big supporter had invested about £2000 on him. Evidently rumor got round that Agricolo was not trying. As I was about to mount, my benefactor said: “Bob, Agricolo is at a longer price now than I got for a big parcel put on him.”
When I told him that he was not likely to catch the books in such a good humor again, he sent his commissioner in to put on another £1000. It was a good thing that he did hear the disquieting rumors, as he would not have backed up otherwise.
He knew that the horse, trainer and rider were O.K., and felt that the danger lay in interference. I told him that nothing would get within a “bull’s roar” of Agricolo to interfere with him, and such was the case.

5-: From the column Let’s talk it over, by J. M. Rohan, published in The Sporting Globe (Melbourne, Victoria) of Wednesday 13^th January 1937:

Memories Of Sailing Home
ON one of his many trips to Australia, Jimmy Hayes brought out Sailing Home. At Mornington last week Jimmy asked Ned O’Dwyer if Sailmaker, who was running in the Welter, was as good as his sire. Ned answered that Sailmaker couldn’t get within a bull’s roar of Sailing Home as a galloper, but that he would go near winning. Sentiment prompted Jimmy to take £10 to £1, and he had the pleasure of collecting.