Generally speaking, you need a physical remote to setup the roku whenever it is new, has been factory reset, or introduce a new network connection (take it on the road or set up new router with different settings).
If you remember your last wifi connection settings (your SSID/network name and password) from your prior network connection, you can set those in your new router and your Roku should connect.
Another take on the above method is to use two mobile devices. (one has the Roku remote app like you have) and then the other you use as a hotspot(if applicable). You then set up the hotspot to have the same network settings as your prior network. Basically, you are using the hotspot in place of the router connection.
However, since you have a bouncing logo rather than the Home Screen Screen, sounds like the Roku may have been reset or is stuck in boot mode.
If you can't remember your previous network name and password, then getting another physical Roku remote is really the only solution. You can get these at Walmart, Target, and Best Buy easily. Since you need one in case you ever have to factory reset your device, probably best advice is to get a remote even if you get connected from one of the above methods. (just in case).
Feel free to post back with an update or if you need more help. Provide Roku model number, router model number, and ISP (internet provider) if needing help with router settings.
Roku Community Streaming Expert
Just another Roku user... I am not a Roku employee.
Insignia RokuTV, Ultra 4660x, Premiere+ 3921, Express 4k+ 3941