Is this a good approach for a BayeuxClient class?
I have no idea how to type the last character on my keyboard which makes modification harder:


public boolean GetIfHandIsShaken£()



It's better to use only ASCII letters.
See Effective Java, 2nd edition, Item 56: Adhere to generally accepted naming conventions and The Java Language Specification, Java SE 7 Edition, 6.1 Declarations:


  Class and Interface Type Names
  
  Names of class types should be descriptive nouns or noun phrases, not overly long, in mixed
  case with the first letter of each word capitalized.
  
  [...]
  
  Names of fields that are not final should be in mixed 
  case with a lowercase first letter and the first letters of 
  subsequent words capitalized.


CometD_Client could have a more descriptive classname too. Every CometD client could have been called CometdClient. Why is it special? Try to put that into the name.

TransportOptions = new HashMap&lt;String, Object&gt;();



This could be in the same line as the declaration:

private Map&lt;String, Object&gt; transportOptions = new HashMap&lt;String, Object&gt;();

HttpClient has a stop() method. I suppose you should call it somewhere.