How do we know that exchanges don't have trading bots going, affecting prices and our trades? There is so much unknown when it comes to an exchange. There are bids and asks constantly flashing. There are lots of people using some sort of trade bot tapped into an exchange's API. 

How can we be sure that the people running the exchange are not doing anything sketchy?
To know what is going on, it is important to understand the order book.

The order book is the set of all open orders on the exchange.
The bids and asks we see flashing indicate changes occurring on the order book.

The order book changes when these happen:

An order is added to the order book (new order is placed).
An order is removed from the order book (order is filled by a trade or order is cancelled).

Since the order book is visible to us, we can check it for any type of sketchy behavior. The order book can be compared with order books on other exchanges. Some services exist that aggregate pricing data from exchanges. See: https://www.cryptocompare.com/coins/btc/markets/USD. If we use a limit order, there is no way for an exchange to manipulate our order or trade. If they did, we would know immediately. This is because we set the limit price of course. Ultimately, exchanges could be doing malicious things behind the scenes and malicious bots could be operating on the outside. In order to know if funny business is occurring, we must understand how the market is supposed to be working. Additionally, we must protect ourselves from the malicious behavior that may exist.
Additional notes on price manipulation:

If an exchange were to manipulate prices materially, they would create an arbitrage opportunity for market participants. As market participants exploited the opportunity, the price would move toward the true price.
If an exchange were to be creating phony bids/asks, aka quote stuffing, it would require analysis of all order submissions to know that this was happening. This data would need to be made available. The SEC provides this type of data for analysis of exchange traded equity securities. This data is provided through the Market Information Data Analytics System. This type of manipulation would not affect users creating limit orders. However, it would allow the exchange to scalp every market order.

We can protect ourselves by:

Using limit orders. When we use a limit order, we set the limit
that we are willing to pay. When we look at the order book, we are looking at all prices available to choose from. At each price there is some quantity available for trade See: GDAX limit order
Avoiding market orders. If we use a market order, the price is not
specified. Thus, any price can be used to fill our order. See: GDAX market order

I have made this video discussing the order book on GDAX.  Take a look here: GDAX order book
This playlist contains the videos mentioned above along with others that may help.
Take a look here: GDAX Playlist