^ I like that idea too, Yellow! Thank you for your input!!!
I came up with a slightly different solution that Worked and played out quite nicely for us:
MY SOLUTION:I decided to use a 4 sided pyramid die. When a player draws a Bazaar tile, they first place that Bazaar tile as normal, THEN roles the 4 sided die INSTEAD of drawing two additional tiles, as the original rules state (2 tiles for a two player game). Under this new modification, the lowest number rolled could be 1, highest being 4. The number that comes up becomes how many Bonus Bazaar tiles are drawn (instead of the standard 2)! The other player still has first choice when choosing from those bonus drawn tiles (possible 1-4). This tile is Now FREE to them (NO BIDDING REQUIRED). The remaining bonus Bazaar round tiles (if any) are then given to the first player, whom initially started the Bazaar sequence. The tiles are then placed as normal. With These alterations to the gameplay, the most Free tiles ( again NO bidding is required any longer when using this new rule modification ) that player will receive would be 3! If the die happened to role a 1, the second player WOULD NOT receive a bonus tile to place, and the Bazaar round is over. Regular gameplay then continues, as normal.
A more detailed example of how it plays out:
Player A draws a tile with a Bazaar. They place it on the board, then rolls the 4 sided die. "3" comes up. Player A pulls 3 tiles from the bag and Player B selects one. Player B places that tile into play, then Player A places both of the remaining 2 tiles on the board. This ends the modified Bazaar sequence and gameplay returns to normal with Player B drawing a tile.We tried this modification last night and it worked Quite well, without the arbitrary 2 player bidding conundrum we seemed to have in the first place!
Thoughts? Give it a try next time you play a two player game using Bazaars!!!
I also decided to try another die involving modification that Also works and adds variety, involvolving The Gold Mines (tiles only) and a 20 sided die (for any number of players). If people are interested in hearing that, I can elaborate on it, as well 
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