Do you have to leave Bisq software open and running if you have posted an offer there?
There is notification for mobile as I know.
Mobile notifications. It is available for iOS and Android:
https://bisq.network/downloads/When you have an opened trade, you need leave your computer running online to get payment details from the trade partner and do the necessary payment from your side to finish that trade. You need to pay attention on the timer before it runs out of time. To be a good trader, you should finish your trade (if the trade partner completes the payment) with your trade partner.
Bisq only gives you notification and details if a bitcoin transaction has its first confirmation on the network.
4. Send payment
Now that you’ve taken an offer, it’s almost time to pay the seller.
First, before showing you the seller’s payment details, Bisq will wait for the Bitcoin network to confirm the trade’s transactions. On average, this takes 10 minutes.
Then, you’ll see a pop-up with the seller’s details. Go ahead and pay the seller through the agreed payment method.
https://docs.bisq.network/getting-started.html#3-confirm-trade