It will rise to close to the bid price otherwise there is...

It will rise to close to the bid price otherwise there is opportunity for arbitrage.

What happens next:
Bidder and Target explanatory documents will be sent to all SH. The Bidder document will seek to convince you their offer is a compelling offer. The Target document will most likely say the best thing for SH to do is to accept the offer because it is the best outcome given the company's circumstances.

Offer acceptance documents will be sent out to each SH. It will contain your holder details, the number of shares you hold, the offer period and the offer consideration and payment terms. If you decide to accept, you let the bidder know how many of your shares you wish to sell them and they will pay you the amount agreed per the offer payment terms and after 90% threshold is achieved. If enough SH accept for the bidder to reach the 90% threshold then compulsory acquisition will kick-in and remaining SH will get whatever the offer price was at the time the threshold was met. Payment terms for those that hold out are sometimes not as attractive as those offered to those who accept, i.e. if you don't accept and the 90% threshold is met then you may need to wait an extra few weeks before you receive consideration for your remaining holding.

Where it gets interesting is when, during the offer period, it becomes apparent to the bidder that the number of acceptances are likely to fall short of the threshold. What I say now is far from a guarantee but, in my experience, when the bidder is falling short, they will usually sweeten their offer. Afterall it's a lot of effort to setup a takeover to walk away from it, especially like in a case like this where they know they're getting a bargain.