As a general rule the more letters of RETAINS you have, the greater the chance of a bonus.
Below are all the bonus words you can make if you have six of those letters, SATIRE, and one other letter.
There are a lot of words, so to make learning easier, perhaps break them down into groups of 10-15 words or by distinct letter groups (i.e SATIRE+A, B, C, D and E).
SATIRE +
A - ARISTAE, ASTERIA, ATRESIA
B - BAITERS, BARITES, REBAITS, TERBIAS
C - ATRESIC. CRISTAE, RACIEST, STEARIC
D - ARIDEST, ASTERID, ASTRIDE, DIASTER, DISRATE. STAIDER, STAIRED, TARDIES, TIRADES, TRADIES
E - AERIEST, SERIATE
F - FAIREST
G - AGISTER, AIGRETS, GAITERS, SEAGIRT, STAGIER, STRIGAE, TIRAGES, TRIAGES
H - HASTIER, SHERIAT
I - AIRIEST, IRISATE
J - nothing
K - ARKITES, KARITES
L - REALIST, RETAILS, SALTIER, SALTIRE, SLATIER, TAILERS
M - IMARETS, MAESTRI, MAISTER, MASTIER, MISRATE, SEMITAR, SMARTIE
N - ANESTRI, ANTSIER, NASTIER, RATINES, RESIANT, RETAINS, RETINAS, RETSINA, STAINER, STARNIE, STEARIN
O - OARIEST, OTARIES, ROASTIE
P - PAIREST, PARTIES. PASTIER, PIASTER, PIASTRE, PIRATES, PRATIES, TRAIPSE
Q - nothing
R - ARTSIER, SERRATI, TARRIES, TARSIER
S - ARSIEST, ARTSIES, SAIREST, SATIRES, TIRASSE
T - ARTIEST, ARTISTE, ATTIRES, IRATEST, RATITES, STRIATE, TASTIER, TERTIAS
U - nothing
V - RAVIEST, TAIVERS, VASTIER, VERITAS
W - WAISTER, WAITERS, WARIEST, WASTRIE
X - nothing
Y - nothing
Z - nothing
98 words in total. 6 letters SATIRE doesn't combine with to make a bonus (J, Q, U, X, Y and Z).