The book that you want to get is
R. B. Madgwick, "Immigration into Eastern Australia 1788-1851"
[originally published in 1937]
republished 1969, and unfortunately still in copyright, not currently
published. I did manage to get one second-hand as it was reputedly used as
a text book.
The rules of the bounty systems were set by government, so should be able
to be pulled from government notices and changed with each scheme. There
was no time limit as I recall or can find in reading, it was about funding
them to come over, and it was less likely that they were able to pay or
maybe even want to pay to go back to the UK. Remember that we are talking
about the poorer (agricultural labourers or other manual tasks) so those
unable to pay their own way, so they either came here and continued to be
poor (no return), or came here and made a fortune, and had no need to go
home to be poor again, plus they were greatly unlikely to be able to buy
land as they rented it from the lord of the manor.
Anyway my (bad) typing below ...
Chapter 8 — The development and control of the Bounty system 1835-1841
... 'The first set of Bounty regulations was contained in a Government
Notice issued at Sydney in October, 1835. The bounties offered were similar
to those subsequently granted by Elliot to Government emigrants. This is
not surprising, for Elliot endeavoured to make his system subserve the
interests of the colonies; and those were presumably expressed in the
regulations governing their own immigration system. The bounties offered
were £30 for a married man and his wife, providing neither was over thirty
yeas of age on embarkation, and £5 for each of their children over twelve
months old. £15 was allowed "for every unmarried female whose age shall be
be below fifteen nor above thirty years, who shall come out with the
consent of the settler or his agent, under the protection of the married
couple, as forming part of the family, and destined to remain with it until
such female be otherwise provided for." A bounty of £10 was granted for
every unmarried male immigrant between eighteen and twenty-five, "brought
out by a settler, who at the same time brings out an equal number of
females, accompanying and attached to a family." All the adult males were
to be either mechanics of farm servants.'
To your other question, about post-1841. That is pretty well when they
stopped and the means changed.
Different schemes in place, for that you will need ...
Ian Pearce and Clare Cowling, "Guide to the Public Records of Tasmania,
Section Four — Records relating to free immigration" (1975) I am unsure
whether this is available, I remember buying the last copy that AOT had
available when I got mine years ago (Yes, I am to blame). It may be
available online or again in book form, I have never checked. It has
prefatory information about immigration, then the records lists.
Hope that all helps.