“What if the EU say we can no longer have those bi-lateral agreements, surely that's a hard Brexit as opposed to a softer one?”
I don't tie up trading agreements (if any are forged) with leaving the EU. In my mind they are separate. I don't think I'm explaining myself very well so I'll try just one more time.
A number of nations have trading agreements with the EU. They have never been EU members nor are they ever likely to be. But nonetheless the EU saw fit to sign an agreement with them. None of those agreements, as far as I know, involve any conditions that go with EU membership and membership of the single market, such as free movement of people, accepting the jurisdiction of the ECJ or making substantial payments to fund the EU budget. I imagine there are common standards agreed for the goods and services traded (which is surely the essence of a trading agreement), but, unlike EU membership, those standards only relate to traders wishing to trade with EU members and not those which don’t.
Other nations have no trading agreement with the EU. Trade carries on between the EU and these nations quite successfully. An example is the USA. Both parties have been trying to sign an agreement for fifteen years but nothing has come of their efforts. But trade still carries on between the USA and EU members.
After Brexit the UK could be in either of those two situations. It may have a trading agreement with the EU, it may not. If no agreement can be reached then that’s that. The UK will simply become a trading partner of the EU but with no trade agreement. The UK should not succumb to any impositions to reach that agreement which any normal nation (such as the USA) would decline. That’s not a “Hard Brexit”. What that is is the UK leaving the EU with no trading agreement existing between us. Dozens of countries are in that position; it’s perfectly normal and they manage perfectly well. Leaving the EU means relinquishing all the advantages and being free of all the obligations.