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According to latest Brexit news, UK is offering a 'compromise' to EU. An article on Bloomberg quotes the British PM as saying

“I hope very much that our friends understand that and compromise in
their turn,” Johnson told his audience in Manchester, northern
England, on Wednesday.

But so far one of the greatest roadblocks to an agreement has been the internal disagreements in UK parliament about what kind of agreement is acceptable.

So from that perspective it looks like the PM should probably present this latest compromise to his own parliament first and get an agreement from them.

But it seems that the approach now is for the UK government to bypass the parliament and negotiate only with the EU in a take-it-or-leave-it fashion. This article quoted a senior British government official as saying:

The EU is obliged by EU law only to negotiate with member state
governments, they cannot negotiate with parliament, and this
government will not negotiate delay.

Question:

Can the UK PM legally bypass the parliament when making a decision with EU based on the reason that "EU is obliged to negotiate directly with the UK government"?

He can negotiate and sign agreements without involving parliament yes, but Parliament will need to ratify the agreement once signed for it to come into force. So far he's negotiating with the EU just as Theresa May did. Once his negotiations were complete and an agreement was signed, it would then need to be brought to Parliament. In May's case she managed to negotiate and signed an agreement with the EU, but in her case Parliament refused to ratify it.

Whether it's wise for him to present negotiating points when he has no idea whether or not Parliament will ratify them is another matter, but he can certainly legally do it.

Specifically in the case of the Brexit process things are a bit different, Section 13 of the EU withdrawal act requires a meaningful vote

1. The documents and an associated statement have been published.
   


2. “The negotiated Withdrawal Agreement and the framework for the future relationship have been approved by a resolution of the House of Commons on a motion moved by a minister of the Crown”.
   


3. A subsequent debate has taken place in the House of Lords.
   


4. Parliament has passed legislation to implement the Withdrawal Agreement.

This means the UK parliament must approve, not simply vote to block, the Withdrawal Agreement. But they must have something to vote on. This is not the PM bypassing Parliament, he must bring a deal approved by the EU Council to Parliament for a vote before it can be enacted

More generally in the UK the Government makes treaties.

Ratifying Treaties

The UK Government is responsible for negotiating, signing and ratifying the 30 or so international treaties involving the UK each year.

The starting point for treaty ratification in the UK is that the Government has the power to make international treaties under its prerogative powers. But this cannot automatically change domestic law or rights, and – as the Supreme Court recently ruled in the Miller case – it cannot make major changes to the UK’s constitutional arrangements without Parliamentary authority.

With regards to the Article 50 process, as mentioned in the quote, this is complicated by the fact it cannot arbitrarily change domestic laws or constitutional law. What this means in general is unclear (to me) as usually a governing party has a majority such that changing domestic law is trivial after concluding a treaty agreement and few treaties include changes to constitutional arrangements.

Further to this, whilst parliament cannot ratify a treaty itself it can prevent ratification under the 2010 Constitutional Reform and Government Act by voting against ratification within 21 days of the treaty being put before it.

If within those 21 sitting days either House resolves that the treaty should not be ratified, by agreeing a motion on the floor of the House, the Government must lay before Parliament a statement setting out its reasons for nevertheless wanting to ratify.

This is a rotating clock, giving the house 21 sitting days to so resolve, then following a Government statement another 21 days to reiterate its opposition continuing on indefinitely.