How much time should I allow for attempting to make a connecting flight departing Bristol, UK on Easyjet and making my connecting flight on Delta Airlines to Detroit, MI, USA at Amsterdam Schiphol Airport? I would have approximately one hour and ten minutes should I attempt to connect with the earliest possible connecting flight with Delta. If I do not make that connection, I would have at least an additional two and a half hour wait for the next available flight. What do you think my chances are of making that first connection?
This is a bad plan. EasyJet and Delta do not interline, so you'd be purchasing two separate tickets. When you do this, you are responsible for arranging your own connection, not the airlines. If you have checked baggage, you'll have to go through immigration, baggage claim, and customs, then go to the Delta counter and check them in before proceeding through security and exit immigration. Since the check-in counter and boarding door close before the departure time, this is not practical to do in 1:10 even if everything is on time.
Because you've arranged your own connection, Delta is not responsible if you miss your flight (even if the easyJet flight is delayed) and could require you to pay a considerable amount of money for a ticket on a later flight and/or incur the costs of a lengthy delay.
Since you are, as your username notes, a "first time traveler in Europe," I'd book this all on one ticket with another airline, even if it costs more, so you don't have to worry about your connection. If you must have two separate tickets, I'd allow several hours to give yourself a cushion for at least some delays; you could consider giving yourself a very long layover and taking the train into Amsterdam for a look-around, as it's a fast and easy trip into the city.
EasyJet does not do connections and does not do 'one ticket' with other airlines or even their own.
So you are on your own if the EasyJet flight is delayed.
I have flown a few times on this route in the last few years and my record of delays runs from nothing to almost 3 hours. With 2 out of 6 journeys with a delay of two to almost three hours.
One time I had an hour wait to pass through passport control in Amsterdam, just because it was busy and there were problems with the automated passport control system.
Based on that I would not book an ongoing flight with 3 hours or less in Amsterdam.
If you can, consider the KLM flights from Bristol, as that company does do 'one ticket' or 'guarantied connection' and you can stay airside in Amsterdam when you have arranged your right tickets.
So it depends on how important your ongoing journey is. If you have to fly EasyJet, consider to fly to Amsterdam a day ahead of time. Or get a single ticket Bristol - Detroit with KLM and Delta.
You have no chance whatsoever of making that connection. Delta will close check-in for the Detroit flight an hour before departure so, if your EasyJet flight is on time, you will have ten minutes to get through immigration, collect your bags and check them in again. In ten minutes, I doubt you'll manage more than getting to the immigration queue.
You mention that, if you miss your connection, there's another flight in two-and-a-half hours. That honestly doesn't help you very much at all. First, that flight is quite likely to be completely full. Second, even if it isn't, you'll have to pay to change your ticket. It is your responsibility to arrive at the airport on time and if you fail to do that, the airline is under no obligation to put you on another flight for free. As far as the airline (in this case, Delta but this applies whenever you have a flight on a separate ticket) is concerned, another airline's plane being late is just the same as the train being late or you setting off too late in your car.
If you haven't already bought these tickets, I strongly recommend that you change your plans. Buy one ticket that covers your whole journey. In that case, you must get to the first airport on time but, then, if a flight on that ticket is delayed, they will put you on the next available flight because it was their fault you missed the connection, rather than yours. Furthermore, with one ticket, your bags will automatically be checked through to your destination and you won't have to go through immigration at Amsterdam.
If you have already bought the ticket from Amsterdam to Detroit, you need to allow much more than an hour for your connection. I would allow at least three hours: you're recommended to check in at least two hours before departure and this allows an extra hour in case your incoming flight is delayed.
The best answer anyone can give is "maybe."
If you're on a single ticket, as @Jim MacKenzie asked, Easyjet would be responsible for your connection to Detroit if you miss the Detroit flight. However, that means waiting for Easyjet to make other arrangements, and then waiting for the other flight, and enduring the accompanying uncertainty and tension, and arriving in Detroit later than planned. Missing the Detroit flight has a significant possibility of really ruining your day.
If I were flying this route, I would elect a later Amsterdam departure. A few extra hours mid-trip would vastly increase the chance of making the Detroit flight, and the entire trip would be easier emotionally. For me, that'd be an attractive tradeoff.