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A person who is "easy to be with" is one with whom you can relax and have a pleasant time. Someone who gets along well with you.
Because she is very very busy, she finds it hard to find spare time to spend with anyone. People may seek out her company. They call her on the phone and ask, e.g. "Will you come to dinner with me tonight?" She may well reply, "I really would love to, but I'm afraid I'm far too busy."
What does the phrase in bold and underlined mean? Thanks.
This phrase means people are trying to get her as their company (in this case 'company' means friend) which means they try to look for a friendship from her. You can guess by the context clue. They give her a call to join them but she refuses.
seek out her company 
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