Daily bounties (with the orange dots next to them) are usually Normal - the Challenging and Heroic ones are most often the reward for daily and weekly project completion.
You can spawn more bounties by completing Hostage Rescue and Public Execution (if you save both hostages) events in the open world, and the bounties they drop are usually the same difficulty as your world difficulty setting, so doing these at Normal difficulty should give you some Normal bounties. It's worth noting that while picking up the bounty dropped by the hostage in these events will activate it immediately, you don't actually have to do it straight away, you can deactivate the bounty and come back to it later (they do disappear eventually, but I think it takes several days).
When the manhunt starts next week, you'll also be able to do the manhunt bounties - they always match your world difficulty (albeit with only one named target per bounty), and you can reset your manhunt progress as often as you like if you want to run them over and over again.