Student or Learner
How to connect semantically one part before comma and other one:
'To Joan's proffer of a week or two at one of Bournemouth's best hotel, she had hesitated.'
Thanks in advance,
There are many rules to use comma. One of which is being explained-which is in applicable to your illustrated sentance.
1. To mark off an introductory Adverb Claus.
Applying the rule to the illustrated sentance
The reason for her hesitation is: Joana's offer, so you have puntuated the sentance correctly to mark off introductory Infinitive Clause (Clause starting with "To").