In the example of "a lot of bears", "of bears" is not a prepositional phrase.  Instead "a lot of" is a modifier to "bears".  You could replace "a lot of" with "twenty", and then it would be clear that the subject is "bears" not "twenty".

Here are 3 examples to illustrate the different uses:

Example 1: "a lot" is modifying a countable noun (e.g. a lot of cows).

"There are a lot of cows in that field".  In this case, you could substitute "a lot" with "twenty", and the sentence would be "There are twenty cows in that field", which would sound perfectly normal, and is the equivalent of using "a lot".  The converse is not true, "There is twenty cows in that field" which just sounds wrong, because it is.

Example 2: "a lot" is modifying a non-countable noun (e.g. a lot of beauty)

"There is a lot of beauty in that painting". In this case, "a lot" refers to a large amount, not a countable amount of units, so "there is (or there's) is appropriate. 

Example 3: There is a 3rd example, which is entirely different, when "lot" means "a particular group, collection or set of things". 

"There is a lot of paintings being sold at the auction."  Here, the subject of the sentence is the lot, meaning a group of paintings, and "of paintings" modifies the subject by describing what is included in the set.  In this case, "there is" is correct as "lot" is singular.